(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f be differentiable on (a,b). Show that f is convex if and only if for every x,y in (a,b), f(y)-f(x)>= (y-x)f'(x)

3. The attempt at a solution

The mean value theorem says that there exists an x' in (a,b) such that f'(x') is the average rate of change of the functions. So I have the equation for that tangent line. I am stuck there.

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# Convexity of functions

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