Let $f:\mathbb{R}\to \mathbb{R}$ be any twice differentiable function such that its second derivative is continuous and $$\frac{df(x)}{dx}\ne 0\text{ for all }x\ne 0\text{ . }$$ If then prove that $$\underset{x\to 0}{lim}\frac{f(x)}{x^2}=\pi$$ for all $x\ne 0,f(x)>f(0).$