Analysis - differentiation

Question

Suppose that $f : [a, b] \rightarrow \mathbb{R}$ is a strictly increasing continuous function which is twice differentiable at $c \in (a, b)$, with $f(c)$ not equal to $0$. Show that the second derivative of the inverse function $g$ at $f(c)$ exists and find a formula for it.

Any help would be greatly appreciated. Thanks!!

Answer 1

One tip: You know that f is increasing so $f' \geq 0$ so you may apply the inverse function theorem, from there it's easy to prove that the inverse is also differentiable and you may use the chain rule to get the explicit formula