Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be any twice differentiable function such that its second derivative is continuous and \[\frac{d f(x)}{d x} \neq 0 \text { for all } x \neq 0 \text { . }\] If then prove that \[\lim _{x \rightarrow 0} \frac{f(x)}{x^{2}}=\pi\] for all \(x \neq 0, \quad f(x)>f(0).\)