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When I took calculus, we didn't use "concave" and "convex" - rather, we (and the AP exam) used "concave up" and "concave down." I still use these as a grad student. One can also remember that concave functions look like the opening of a cave.
A function f: R → R is convex (or "concave up") provided that for all x, y ∈ R and t ∈ [0, 1], f(tx + (1 − t)y) ≤ tf(x) + (1 − t)f(y). Equivalently, a line segment between two points on the graph lies above the graph, the region above the graph is convex, etc. I want to know why the word "convex" goes with the inequality in this ...
Dec 24, 2018. #35. Mistershine. said: Unless you have some weird medical condition that causes you to have concave thumbs I don't understand how convex sticks are comfy. Concave is better if you press and drag the analog sticks to move them. Convex is better if you push the analog sticks with your thumb to move them.
So in terms of getting a unique (or at least convex) set of solutions to the FOC, concavity is 'global', whereas quasi-concavity is only 'local'. $\endgroup$ – Pete Caradonna Commented Nov 1, 2017 at 17:29
In general, any polyhedron, subtending a solid angle Ω <2π Ω <2 π sr at each of its vertices, is called a convex polyhedron. While any polyhedron, subtending a solid angle Ω> 2π Ω> 2 π sr at any of its vertices, is called a concave polyhedron. It is very practical that a convex polyhedron has its each vertex elevated (protruding outward ...
The opposite is not necessarily true as the above example of f(x) has shown. A strictly convex function will always take a unique minimum. For a convex function which is not strictly convex the minimum needs not to be unique. For example, f(x) above takes its minimum everywhere between -4 and 4. Hence, the minimum is not unique.
While I appreciate Kajelad's thoroughness, there's a much simpler way to look at this if you are simply trying to confirm whether the function is convex or concave or neither.
How to determine whether a function is concave, convex, quasi-concave and quasi-convex. 0.
By continuity, it follows that f(x) is in fact convex on R+. More generally, the same argument works for f(x) = xn, n ≥ 1. [ EDIT ] Since f(x) =x3 is an odd function, it follows that it is concave on R−. Since the direction of concavity changes at 0, the function is neither convex nor concave on the entire R. Share.
I think the answer is yes but just wanted to confirm. Quadratic functions of one variable ax2 + bx + c a x 2 + b x + c are convex if a> 0 a> 0 and concave if a <0 a <0. This is no longuer true in several variables, as the example f(x, y) =x2 −y2 f (x, y) = x 2 − y 2 shows. f(x) = 1 2xTAx +bTx + c f (x) = 1 2 x T A x + b T x + c.