How Feynman's path integral lead to least action principle? Math proof needed

Question

I have read about Feynman path integral which leads to classical limit. It said that because $\hbar \rightarrow 0$ in classical view. The function of path integral $\int e^{\frac{1}{\hbar}f(x)} dx$ will have very large frequency and only path which $\frac{d f(x)}{dx} = 0$ will not be destructed. However, I cannot find mathematical proof. Could you help me derived it?

Answer 1

You can look up "Laplace approximation" for integrals. In the path integral formalism the word "instanton" is also used.