(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assume that f is a differentiable function such that f(0)=f'(0)=0 and f''(0)>0. Argue that there exists a positive constant a>0 such that f(x)>0 for all x in the interval (0,a). Can anything be concluded about f(x) for negative x's?

2. Relevant equations

3. The attempt at a solution

I think I should use the MVT so here is what I tried:

[tex]f'(c) = \frac{f(a) - f(0)}{a-0}[/tex]

f(0)=0 is given so:

[tex]f'(c) = \frac{f(a)}{a}[/tex]

Now I am confused on how to relate this to f(x)>0.

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# Homework Help: Assume f(0)=f'(0)=0, prove there exists a positive constant such that f(x)>o

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