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Let $f$ and $g$ be functions such that $f''$ and $g''$ exist. Let, for some $a$c \in (a,b)$ such that

$$\frac{f(c)}{g(c)}=\frac{f''(c)}{g''(c)}$$

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    Please give it a look! http://meta.math.stackexchange.com/questions/1803/how-to-ask-a-homework-question2012-10-30

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Let $$h(t)=f(t)g'(t)-g(t)f'(t),$$ and apply Rolle's theorem.

(This assumes $g\ne0$ on $(a,b)$ as well.)