Given f(0)=f’(0)=0, f’(x)>0, x>0

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

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

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## 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 .