Suppose $\displaystyle g:\mathbb{R}\rightarrow{\mathbb{R}}$ is a twice differentiable function with $\displaystyle g(0)=g'(0)=0$ and $\displaystyle g''(0)=14$. Let $\displaystyle f:\mathbb{R}\rightarrow{\mathbb{R}}$ be defined by

$\displaystyle f(x)=\frac{g(x)}{x}$ if $\displaystyle x\neq{0}$, $\displaystyle 0$ if $\displaystyle x=0$

Prove that $\displaystyle f$ is differentiable at $\displaystyle x=0$ and find $\displaystyle f'(0)$.

Can we use L' Hopital's Rule to solve this question?