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!!

Results 1 to 4 of 4

- May 12th 2010, 04:24 AM #1

- Joined
- Nov 2007
- Posts
- 15

- May 12th 2010, 11:52 AM #2

- May 14th 2010, 01:56 AM #3

- Joined
- Nov 2007
- Posts
- 15

- May 14th 2010, 02:46 AM #4
The only reason that you need the condition f''(x)>0 (for x>0) is that it implies that f'(x) is a strictly increasing function, so that f'(x+y) > f'(x) when y>0.

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.