Let's assume that f:[0,∞[ -> R is differentiable twice and f(0)=0 and f''(x)>0, when x>0.
Show that f(x)+f(y)<f(x+y) when x,y>0.
It's really important that I get this done, so any help is highly appreciated!!
The value of f''(x) when x=0 is not relevant. The fact that f''(x) > 0 when x>0 does in fact imply that f is strictly convex.