Given f(0)=f’(0)=0, f’(x)>0, x>0

Show: f(x)>0, x>0 using std calculus (no abstract symbolism please).

Results 1 to 2 of 2

- Oct 5th 2013, 06:01 AM #1

- Joined
- Aug 2010
- Posts
- 961
- Thanks
- 98

- Oct 5th 2013, 06:45 AM #2

- Joined
- Nov 2010
- Posts
- 1,979
- Thanks
- 799

## Re: f(0)=f’(0)=0, f’(x)>0, x>0 -> f(x)>0, x>0

Question: Is continuous on and differentiable on ? (This is true for ).

If so, then we can apply the Mean Value Theorem. Let . By assumption, is continuous on and differentiable on , so by the Mean Value Theorem, there exists such that:

Solving for , we have . Since , we are given that . The product of two positive real numbers is positive, so .