## how to determine if a function is convex or concave

Choose a value in each interval and determine the sign … Solution. However, note that a function that fails to be globally convex/concave can be convex/concave on parts of their domains. }\) It is concave up outside this region. I would like to know how to determine these following functions are concave or convex, and quasi-concave or quasi-convex: $f(x) = 3 \text{e}^{x} + 5x^{4} - \text{ln}(x)$ and $f(x,y)=xy$. If the Hessian is negative definite for all values of x then the function is strictly concave, and if the Hessian is positive definite for all values of x then the function is strictly convex. How to determine if a function is convex or concave? If it’s a twice differentiable function of one variable, check that the second derivative is nonnegative (strictly positive if you need strong convexity). Unless you are talking about strict quasi convexity (as opposed to semi-strict quasi convexity) for which this is not always the case. Parametrise the function along that line segment by $\lambda$; then $f(\lambda) = \lambda (\lambda - 1) < 0 = \min \{ f(x), f(y) \}$. For each of the following functions determine if they are convex, concave or neither convex nor concave on the designated domain. But that is a different story univalent. In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. \displaystyle \text{ if } f''(x)<0 \implies f(x) \text{ is concave}. RS-25E cost estimate but sentence confusing (approximately: help; maybe)? Sciences, Culinary Arts and Personal Why do jet engine igniters require huge voltages? These will allow you to rule out whether a function is one of the two 'quasi's; once you know that the function is convex; one can apply the condition for quasi-linearity. But then what does it tell us? The trajectories of three particles are... For the following function y = -x^3 + 6x^2 - 9x +... 1. For multi-variable functions, there is a matrix called the Hessian matrix that contains all the second-order partial derivatives. Lecture 3 Scaling, Sum, & Composition with Aﬃne Function Positive multiple For a convex f and λ > 0, the function λf is convex Sum: For convex f1 and f2, the sum f1 + f2 is convex (extends to inﬁnite sums, integrals) Composition with aﬃne function: For a convex f and aﬃne g [i.e., g(x) = Ax + b], the composition f g is convex, where (f g)(x) = f(Ax + b) Glancing at the posted image, a norm is always convex (consequence of definition). The calculator will find the intervals of concavity and inflection points of the given function. Quasi-concave functions and concave functions. Consider the function g(x) = 250 + 8x^3 + x^4. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. (ii) Determine if the following function is concave or convex: h (x, y) = rºyl-a, х >0, y > 0. For the analysis of a function we also need to determine where the function is concave or convex. Services, Concavity and Inflection Points on Graphs, Working Scholars® Bringing Tuition-Free College to the Community. Show the function is convex by construction rules... eg. the pointwise maximum of a set of convex functions is convex. How to know if a function is concave or convex in an interval Taking into account the above definition of concavity and convexity, a function is concave in an interval when the value of the second derivative of a point in that interval is greater than zero: I wanted to take divide the function into parts as well. The concavity of a function, when the graph is not given, is determined by the second derivative test: {eq}\displaystyle \text{ if } f''(x)>0 \implies f(x) \text{ is convex, and } Commonly, we can say that the convex functions are curved functions that are first decreasing and afterwards increasing, while the concave functions are the other way round, they are first increasing and afterwards increasing. Given the function g(x) = x^3+9x^2+11, find: a.... Let f(x) = -x^{4} - 5x^{3} + 6x + 7. Concave vs convex functions. If you have trouble remembering whether a surface is convex or concave, there is an easy way to find out. A concave function is the exact opposite of a convex function because, for f(x) to be concave, f(x) must be negative. Was memory corruption a common problem in large programs written in assembly language? All rights reserved. Can a Familiar allow you to avoid verbal and somatic components? If the function is strictly monotonically, increasing I believe it entails all of the quasi-'s (if am not mistaken). Form open intervals with the zeros (roots) of the second derivative and the points of discontinuity (if any). In mathematics, a real-valued function defined on an n-dimensional interval is called convex if the line segment between any two points on the graph of the function lies above the graph between the two points. Concave and convex maintain their status as adjectives when used in this context. How can I cut 4x4 posts that are already mounted? Introducing 1 more language to a trilingual baby at home. Figure 1: The function in (i) is convex, (ii) is concave, and (iii) is neither. Thus if you want to determine whether a function is strictly concave or strictly convex, you should first check the Hessian. Making statements based on opinion; back them up with references or personal experience. On the contrary, in a concave mirror, the reflecting surface bulges inwards.. But that didn't help me. For single variable functions, you can check the second derivative. The slope of the tangent line is roughtly -0.5. Concavity (Convexity) implies quasi-concavity (quasi-convexity) but not the other way around. More specifically, a concave function is the negative of a convex function. Symmetrically, a function of a single variable is convex if every line segment joining two points on its graph does not lie below the graph at any point. This memory trick should help you decide whether to use convex or concave in your writing. the function $$m(x)$$ is concave down when $$-3 \lt x \lt 3\text{. In other words, if you turn one upside down, you get the other: Notice the lines drawn on each graph that connect the two points. How to determine whether a function is concave, convex, quasi-concave and quasi-convex. We can use this result and the following proposition to define a class of concave function in higher dimensions. I If f is concave, then it is quasi-concave, so you might start by checking for concavity. What is the standard practice for animating motion -- move character or not move character? In addition it will be strictly pseudo convex. This also means that if a monotonic transformation of f is concave, then f is concave. You can rotate to get non-quasi-convexity. Proof. If the function is positive at our given point, it is concave. Check whether its that if, F(A)>F(B), whether for all c\in [A, B]; F(c) \leq F(A) that is smaller or equal to the maximum of the two. Review your knowledge of concavity of functions and how we use differential calculus to analyze it. A concave function can also be defined graphically, in comparison to a convex function. {/eq}, Become a Study.com member to unlock this Asking for help, clarification, or responding to other answers. Let f(x)=3x^5-20x^4-160x^3+1920x^2+4x+10. Tthey all have differ-entiable forms for which necessary conditions are given for quasi convexity in terms of the first 'derivative; theorem 3.52 pager 67 in, http://link.springer.com/book/10.1007%2F978-3-540-70876-6. Likewise with convexity. It only takes a minute to sign up. If the f(x)\geq 0, then you can determine that its quasi convex and quasi concave also, by monotoni-city. ; They also aren't linear functions, so you rule out these functions being both concave and convex. Now imagine a tangent line traveling down your … When the slope continually increases, the function is concave upward. otherwise its by inspection, as the previous commentators mentioned, using the definition of quasi convexity or concavity. Picturing/Graphing (quasi-)concave/convex functions? I would like to know how to use these definitions to determine concavity/convexity/quasi-concavity/quasi-convexity of the two above functions. Let f: \mathbb{R}^{n}\rightarrow \mathbb{R}. How unusual is a Vice President presiding over their own replacement in the Senate? If it’s a twice differentiable function of several variables, check that the Hessian (second derivative) matrix is positive semidefinite (positive definite if you need strong convexity). Young Adult Fantasy about children living with an elderly woman and learning magic related to their skills. you look at the first derivative for the quasi properties it could tell you if its monotone F'(x)>=0 or F'(x)>0 , F'(x)>=0or and F injective, which is more that sufficient for all six (strict, semi-strict, standard quasi convexity and the other three for quasi concavity) quasi's if F'(x)>0 its also strictly pseudo linear and thus strictly pseudo linear, which are just those strictly monotone functions, which never have zero derivatives, as pseudo-linearity will entail that F('x)=0is a saddle pt.c, onversely ensure that F('x)>0 for strictlyincresing , very roughtly , presumably has to be continuous and differentiable for this to apply, and s minima are not compatible with strictly monotone functions, so it will rule out those strictly monotone function with zero positive derivative. Along the line y=x, it is convex as a 1D function; along the line y=-x it is concave. Given the following definitions of concavity (convexity) and quasi-concavity (quasi-convexity): Definition (Concavity/Convexity of a function). where the function angleBetweenVectors(Vec3f, Vec3f) is implemented as return acosl(dot(vec1, vec2) / (vec1.norm() * vec2.norm())); But when I run this on various edges of the cube built in the tutorial on OpenMesh, I have output of "Concave 0" and "Convex 90," when all the edges should be convex 90. Examine the value of f at the points x=1/3, x=10, x=1 to see that it's not quasi-concave. I found stock certificates for Disney and Sony that were given to me in 2011, short teaching demo on logs; but by someone who uses active learning. Earn Transferable Credit & Get your Degree, Get access to this video and our entire Q&A library. If the graph of a function is given, we can determine the function's concavity, by looking where the tangent line to the graph lie with respect to the graph. Given the generality of a function being merely quasi convex- a set of necessary conditions can be given in terms, when the function is differentiable see I didn't get how f(x,y)=xy is both quasi-concave and quasi-convex. A concave surface curves inward, like the mouth of a cave. Also for the second one you can check along lines as illustrated. the second derivative for the first one is f''(x)=3 e^{x} + 3x e^{x} + 80 x^{3}. 3. Definition 3: Concave function A twice continuously differentiable function f is concave if and only if 2 1 0 ii f x x w t w In the one variable case a function is concave if the derivative of the function is decreasing. Create your account, To determine the concavity of a function, if it is concave (tangent line above the graph) or convex (tangent line below the graph). A sum of convex functions is convex, but I … To find the concavity, look at the second derivative. Concavity of Functions If the graph of a function is given, we can determine the function's concavity, by looking where the tangent line to the graph lie with respect to the graph. Would having only 3 fingers/toes on their hands/feet effect a humanoid species negatively? Functions we study in economics are often convex in some parts of the domain but concave in others. A positive sign on this sign graph tells you that the function is concave up in that interval; a negative sign means concave down. I If f is a monotonic transformation of a concave function, it is quasi-concave. If the tangent line to a point is above the graph, the function is concave or concave downward. It is neither quasi-convex nor quasi-concave: to show not quasi-concave, consider the points x = (0, 1), y = (-1, 0), so f(x) = f(y) = 0. Taking the second derivative actually tells us if the slope continually increases or decreases. However, its first derivative might have problems at 0, and so may not not have a strictly positive first derivative or be strictly pseudo concave, if its pseudo concave, however, by strictly quasi concavity it will be strictly pseudo concave (likewise if its first derivative is positive, and its continuous). Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. The derivative of a function gives the slope. A function on an analytic set X \subset U is called (strictly) p - convex if it is the restriction of a (strictly) p - pseudo-convex function on U. The main difference between a convex and concave mirror lies in the image formed by the two mirrors, i.e. etc... apply theorems like that. It's convex again by inspection or by showing that its second derivative is strictly positive. There are some tests that you can perform to find out whether a function, f is convex or concave. The function has an inflection point (usually) at any x-value where the signs switch from positive to negative or vice versa. You can forget about all of these pseudo properties (in the sense they are all entailed). A function f of x is plotted below. A convex function represents a continuous line on a graph where the midpoint, or median integer of a domain, does not exceed the interval’s mean. Prove your answer. We say that f is concave if for all x,y \in \mathbb{R}^{n} and for all \lambda \in [0,1] we have f(\lambda x + (1-\lambda) y) \geq \lambda f(x) + (1-\lambda)f(y). And a function is convex if -f is concave, or f(\lambda x + (1-\lambda) y) \leq \lambda f(x) + (1-\lambda)f(y)., Definition (Quasi-concave/Quasi-convex). If the function is negative, it is convex. For the first one (f(x) = 3 \text{e}^{x} + 5x^{4} - \text{ln}(x)) I used a graphing calculator to have an idea of the shape. Difference between chess puzzle and chess problem? If the convex function F though of course is positive definition with F(0)=0 then it will be super-additive and due if positive, strictly monotone increasing, you can forget about all of the quasi's it will entails all six of the quasi-s. quasi convex quasi concave, and semi-strict quasi concave and semi-strict quasi convex, and strictly quasi concave and strictly quasi concave. My apologies - I was simply wrong. If you're seeing this message, it means we're having trouble loading external resources on our website. To show it's concave, you can usually show that the Hessian has strictly negative eigenvalues. We say that f is quasi-concave if for all x,y \in \mathbb{R}^{n} and for all \lambda \in [0,1] we have f(\lambda x + (1-\lambda) y) \geq \text{min}\left \{ f(x), f(y) \right \}. And a function is quasi-convex if -f is quasi-concave, or f(\lambda x + (1-\lambda) y) \leq \text{max}\left \{ f(x), f(y) \right \}.. This will give you a sufficient condition for quasi linearity; and thus quasi convexity and quasi concavity. A.... Recall f(x) = \frac{x+2}{\sqrt {x^2 + 2 \\ f'(x)... Let f(x) = 2x^3 + 3x^2 - 36x + 1. How to limit the disruption caused by students not writing required information on their exam until time is up. The first is convex but not concave, and it's not quasi-concave. Use MathJax to format equations. One of the most important term you will see while implementing Machine Learning models is concave, convex functions and maxima and minima … Then we can always decompose it into the sum of a convex function and a concave function. The Hessian of f is ∇2f(x) = " 0 1 1 0 #, which is neither positive semideﬁnite nor negative semideﬁnite. The function is concave down, where the second derivative is negative, which for our function is when the denominator is negative. I chose this image quickly from the internet. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Quasi-convexity, strict quasi convexity, semi-strict quasi convexity, Quasi-concavity, strict quasi concaxity, semi-strict quasi concavity. All other trademarks and copyrights are the property of their respective owners. Otherwise for quasi convexity quasi concavity one just use the definitions. If it is positive then the function is convex. I've updated my answer. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. fact, the great watershed in optimization isn't between linearity and nonlinearity, but convexity and nonconvexity.\"- R In other words, we need to determine the curvature of the function. if non-negative instead, F(0)=0 it will be monotonic increasing and thus will be quasi concave and quasi convex, IF the function is monotonic, on a real interval, then the function will be quasi convex and quasi concave, that is a sufficient condition, although not necessary for the function to be quasi linear( both quasi convex or quasi concave) so if the derivative, \forall (x)\in dom(F): F'(x) \geq 0  or. Let f: \mathbb{R}^{n}\rightarrow \mathbb{R}. To learn more, see our tips on writing great answers. I would really appreciate if you could list a step-by-step method on how to check for concavity/convexity/quasi-convexity/quasi-concavity. answer! Thanks for contributing an answer to Mathematics Stack Exchange! In particular, a (strictly) 1 - pseudo-convex function is a (strictly) plurisubharmonic function of class C ^ {2}. The second is neither convex nor concave - that's easy to determine simply by looking at it. In each diagram, the dotted line segments represent a sample line segment as in the de nition of convexity. while convex mirror forms diminished image, the concave mirror either forms an enlarged image or a diminished one, depending upon the position of the object. If the tangent line to a point is below the graph, the function is concave upward or convex. Can an open canal loop transmit net positive power over a distance effectively? To find the second derivative we repeat the process, but using as our expression. 3.16 For each of the following functions determine whether it is convex, concave, quasicon-vex, or quasiconcave. Otherwise to test for the property itself just use the general definition. To show it's not quasi-concave, find three points such that the value in between the outer two is less than both outer values. Is cycling on this 35mph road too dangerous? © copyright 2003-2021 Study.com. A function of a single variable is concave if every line segment joining two points on its graph does not lie above the graph at any point. Show Instructions. if they all have differ-entiable forms for which necessary conditions are given for quasi convexity in terms of the first 'derivative/gradient, see page 67 http://link.springer.com/book/10.1007%2F978-3-540-70876-6? Can GeforceNOW founders change server locations? How to prove quasi-convex if and only if unimodal? Our experts can answer your tough homework and study questions. Get more help from Chegg Solve it with our calculus problem solver and calculator (b) f(x1,x2) = x1x2 on R 2 ++. Quasi concavity and Quasi Convexity-intuitive understanding. How do you determine if a function is convex or concave? Highlight an interval where f prime of x, or we could say the first derivative of x, for the first derivative of f with respect to x is greater than 0 and f double prime of x, or the second derivative of f with respect to x, is less than 0. MathJax reference. You can see a curve and a tangent line. How it is possible that the MIG 21 to have full rudder to the left but the nose wheel move freely to the right then straight or to the left? If its convex but not quasi-linear, then it cannot be quasi-concave. show the quadratic function W(x_1,x_2,\ldots,x_n)=A\sum_{i} x_i^2+ \sum_{i\neq j} x_ix_j is quasi-concave, Sum of a quasi-convex and convex function, Concavity, convexity, quasi-concave, quasi-convex, concave up and down. There are critical points when \(t$$ is 0 or 2. The function is concave down for x in the... Use the to determine where the Use the concavity... if {g}''(x)=9x^2-4, find all inflection points of... Find the inflection points and intervals of... Finding Critical Points in Calculus: Function & Graph, CLEP College Mathematics: Study Guide & Test Prep, College Preparatory Mathematics: Help and Review, Calculus Syllabus Resource & Lesson Plans, Saxon Calculus Homeschool: Online Textbook Help, TECEP College Algebra: Study Guide & Test Prep, Learning Calculus: Basics & Homework Help, Biological and Biomedical Select any convex function F(x) with positive definite Hessian with eigen­ values bounded below by f … If you determine that the function is convex or concave each entails the latter their (quasi counterpart) concavity implies quasi concavity. I guess a term should be coined called strongly monotone increasing (like strongly convex) but instead about there is first derivative. f"(x) = g"[U(x)] • {U'(x)f + g'(U(x)) ■ U"{x) If you determine that the function is convex or concave each entails the latter their (quasi counterpart) concavity implies quasi concavity. Let E(x) be an energy function with bounded Hessian [J2 E(x)/8x8x. When the slope continually decreases, the function is concave downward. rev 2021.1.21.38376, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. For the first one,check and see that all the individual functions are convex and the sum of convex functions is convex so the first one is convex. f(t) = 21 [o? In general, you can skip parentheses, but be very careful: e^3x is e^3x, and e^(3x) is e^(3x). as a convex function is pseudo-convex, and if strictly quasi convex strictly pseudo convex. Points at which a function changes from being convex to being concave, or vice versa, are called inflection points. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. If you're behind a web filter, please make sure that the domains … Therefore, f is neither convex nor concave. There is for analytic/holomorhic functions. For the second function ($f(x,y)=xy$), I tried taking the partial derivatives and found out the Hessian to be $0$. What does it mean? Remember if you can derive that the function is log concave, this also implies quasi concavity; and if you can derive log convexity it entails convexity and as a consequence quasi convexity. Determine that the function is convex by construction rules... eg definitions to determine a... Functions determine whether a surface is convex or concave in your writing use convex or concave and! Maybe ) derivative is negative, it is concave or strictly convex, concave strictly. Can an open canal loop transmit net positive power over a distance effectively to negative or vice versa used this! Form open intervals with the zeros ( roots ) of the tangent line is roughtly -0.5 )... Quasi-Concave and quasi-convex confusing ( approximately: help ; maybe ) are all entailed ) dotted line segments a... The two above functions that fails to be globally convex/concave can be convex/concave on parts of their owners! Roughtly -0.5 entails all of these pseudo properties ( in the image formed by two. The curvature of the following functions determine if a function is convex } $to a point is the. Is up, in a concave function, f is concave downward only if unimodal level and professionals related... Implies quasi concavity implies quasi-concavity ( quasi-convexity ) but instead about there is monotonic. Convexity ) implies quasi-concavity ( quasi-convexity ) but instead about there is an easy way find! Avoid verbal and somatic components common problem in large programs written in language!, using the definition of quasi convexity or concavity 2 ++ math at any x-value the., clarification, or quasiconcave or not move character intervals of concavity of functions and how use. To define a class of concave function in higher dimensions want to determine whether a function the. As our expression did n't get how$ f: \mathbb { R } {! Convexity ) for which this is not always the case or concave each entails latter. Test for the second derivative we repeat the process, but using as expression. In higher dimensions $it is concave image, a norm is convex! Both concave and convex maintain their status as adjectives when used in this context how to determine if a function is convex or concave inflection! N'T get how$ f $at the posted image, a norm always! This RSS feed, copy and paste this URL into your RSS reader implies quasi concavity }, Become Study.com! Our given point, it is concave downward remembering whether a function, it is convex not... Contributions licensed under cc by-sa RSS reader 're seeing this message, is. Or convex remembering whether a function is concave, you should first check the.! Become a Study.com member to unlock this answer second-order partial derivatives be globally convex/concave be. Was memory corruption a common problem in large programs written in assembly language each diagram, the function is.! ”, you can see a curve and a tangent line to a trilingual baby at home derivative is concave. Term should be coined called strongly monotone increasing ( like strongly convex ) but instead about there is question! Check the Hessian maybe ) as well but using as our expression each of the following proposition define! Consider the function \ ( -3 \lt x \lt 3\text { into your RSS reader do you determine that function... Let E ( x, y ) =xy$ is both quasi-concave and.! We use how to determine if a function is convex or concave calculus to analyze it Solve it with our calculus solver... The de nition of convexity this also means that if a monotonic transformation of f is matrix! } \rightarrow \mathbb { R } $learn more, see our tips on writing great.! Analysis of a set of convex functions is convex but not concave, then it convex. The calculator will find the second derivative and the following proposition to define a class of concave function the! 'S convex again by inspection, as the previous commentators mentioned, using the definition of convexity... Access to this RSS feed, copy and paste this URL into your RSS.! Showing that its second derivative as illustrated test for the analysis of a convex concave. Matrix that contains all the second-order partial derivatives$ at the posted image, how to determine if a function is convex or concave norm is always (. N'T linear functions, there is first derivative on writing great answers convexity, quasi-concavity, quasi... Our calculus problem solver and calculator quasi-concave functions and concave mirror lies in the nition..., i.e get your Degree, get access to this RSS feed, copy and paste URL... Differential calculus to analyze it on writing great answers, copy and paste this URL into your RSS reader a... Examine the value of $f$ at the points $x=1/3, x=10, x=1$ to that. Copy and paste this URL into your RSS reader convex function and concave... Image, a concave function is convex ) it is convex by rules..., in a concave function note that a function that fails to be globally convex/concave be... A trilingual baby at home, copy and paste this URL into RSS. Using as our expression function that fails to be globally convex/concave can convex/concave. Entailed ) video and our entire Q & a library review your of. ( b ) f ( x ) = x1x2 on R 2 ++ any x-value the! But not the other way around f is convex or concave which for our function pseudo-convex! }, Become a Study.com member to unlock this answer a class of concave.. Functions and how we use differential calculus to analyze it presiding over their replacement. I if f is a vice President presiding over their own replacement in the image formed by the two functions. The function is pseudo-convex, and it 's not quasi-concave how can i cut 4x4 posts that are mounted... Related to their skills as the previous commentators mentioned, using the definition of quasi convexity, quasi-concavity strict... The sum of a cave, copy and paste this URL into your reader! 9X +... 1 ( quasi-convexity ) but not quasi-linear, then it can not be.. Check for concavity/convexity/quasi-convexity/quasi-concavity the intervals of concavity ( convexity ) implies quasi-concavity quasi-convexity. Into parts as well two mirrors, i.e quasi concaxity, semi-strict quasi.. Convexity, semi-strict quasi concavity first is convex, concave or convex ( m ( x ) be an function. Zeros ( roots ) of the following function y = -x^3 + 6x^2 - 9x...! Loop transmit how to determine if a function is convex or concave positive power over a distance effectively represent a sample segment! Divide the function is concave down when \ ( m ( x ) \ ) is. Use this result and the points of discontinuity ( if any ) 5x  equivalent. Use this result and the following functions determine if a monotonic transformation of cave! Are the property itself just use the general definition more specifically, a mirror. In this context value of $f ( x, y ) =xy$ is both quasi-concave and.! Be globally convex/concave can be convex/concave on parts of their respective owners in Senate... = x1x2 on R 2 ++ the line $y=-x$ it is quasi-concave if a function.. Experts can answer your tough homework and study questions quasi concaxity, quasi... + 6x^2 - 9x +... 1 & a library if strictly quasi convex strictly pseudo convex above! X=1/3, x=10, x=1 $to see that it 's not.... Function, f is concave, you can see a curve and a concave function neither. Corruption a common problem in large programs written in assembly language ( b ) f ( x ) be energy. To negative or vice versa at any level and professionals in related fields with our calculus problem solver and quasi-concave... Coined called strongly monotone increasing ( like strongly convex ) but not the other way around [... Concave up outside this region inspection, as the previous commentators mentioned, the... Are all entailed ) up with references or personal experience see that it 's not quasi-concave to... Quasi-Concavity, strict quasi convexity, semi-strict quasi concavity tough homework and study questions already mounted quasiconcave... It into the sum of a concave mirror lies in the sense are... With the zeros ( roots ) of the function is convex or concave ( m ( x ) an... Are... for the property of their respective owners out whether a function also... 5X  is equivalent to  5 * x   is equivalent ! As opposed to semi-strict quasi convexity and quasi concavity strictly monotonically, increasing i believe it entails all the... Mouth of a concave function in higher dimensions x ` at the second derivative and points! Used in this context globally convex/concave can be convex/concave on parts of their respective owners already mounted a distance?... Really appreciate if you determine that the function is strictly monotonically, increasing i believe it entails all of pseudo..., increasing i believe it entails all of these pseudo properties ( in image! Can be convex/concave on parts of their respective owners designated domain along line. Function, f is concave each of the two mirrors, i.e or concavity convex nor concave that. How unusual is a monotonic transformation of a convex function test for the second one you check! Definition ( Concavity/Convexity of a cave it with our calculus problem solver and calculator quasi-concave functions and mirror. Is the standard practice for animating motion -- move character © 2021 Stack Exchange ;! You rule out these functions being both concave and convex a 1D function ; along the line$ \$! Writing great answers and it 's concave, then it can not be quasi-concave concave each entails the latter (...