How to prove a function is concave? (Single Variable)
Proposition A twice-differentiable function f of a single variable defined on the interval I is concave if and only if f ''(x) ≤ 0 for all x in the interior of I convex if and only if f ''(x) ≥ 0 for all x in the interior of I.
convex analysis - Product of concave functions is concave
2019年5月2日 · Tour Start here for a quick overview of the site
mnemonic - How to remember which function is concave and …
2017年7月20日 · In English, there is a great trick from David MacKay's recommended book on information theory: Just keep pronouncing the word "convex" as "convec-smile" and "concave" as "conca-frown" and the direction of the mouth of the corresponding smiley will tell you what the graph of the function looks like.
Defintion of strictly concave - Mathematics Stack Exchange
2018年11月26日 · EDIT: I see a counterexample in the comment. I have now corrected the errors in my question (mixed up strictly concave and concave) and broadly ask about when I can use the second derivative to prove concavity (as is done to show $\log(x)$ is concave for instance) and how the equivalence is shown in these cases.
real analysis - Subtracting convex function from concave function ...
2019年9月15日 · Subtracting convex function from concave function. Ask Question Asked 5 years, 3 months ago.
calculus - How to understand concave function definition?
2017年1月26日 · I am trying to understand concave functions, for which wikipedia gives an expression written as: now I am confused as how to understand this as the line over there says that this definition merely states that for every z between x and y, the point (z, f(z) ) on the graph of f is above the straight line joining the points (x, f(x) ) and (y, f(y) ).
calculus - simple concave two-variable function - Mathematics …
2021年2月9日 · The increasing rate of an increasing strictly concave function 0 Is a concave parametric curve along a concave surface guaranteed to be concave along another concave surface?
optimization - Known concave down increasing function that can …
The estimation will find the function that best fits the data. Theory specifies that the function must be concave down and increase. Here is an image for reference: On the left is what I am looking for. The function can be steep and approach 1 on the Y-axis very quickly or the function can be much flatter. It just has to be concave down and ...
optimization - Concave function divided by a convex function.
The concave function is the geometric mean, and the convex function is the arithmetic mean. Their ration is always between 0 and 1 btw. Does that make a difference? $\endgroup$
conditions for Product of convex and concave function to be …
How to determine whether a function is concave, convex, quasi-concave and quasi-convex. 1.