Concavity

Convexity and Concavity Exercise 1 Show that a function $ f $ is convex on an interval if and only if for all $ x, y $ in the interval and $ 0 < t < 1 $, we have: $$ f(tx + (1 - t)y) \leq tf(x) + (1 - t)f(y). $$Exercise 2 Let $ f $ and $ g $ be convex functions with $ f $ increasing. ...