yet another smooth function problem

Oct 2008
11
0
surprised there have been a few lately, but i need help with the following:

let f(x) be a smooth real-valued function for x in [0,1].

if f(0) = 0, f(1) = 0, and f"(x) is positive for x in [0,1], prove that f(x) <= 0 for x in [0,1].
 
Jul 2008
144
0
f is a strict convex function.
so,...
 
Oct 2008
11
0
so it is strictly convex on [0,1] since f" is strictly positive on the interval. but how does this imply f <= 0 for x in [0,1]?