Let $f$ be twice continuously differentiable in a neighborhood of a point $x^{∗} \in R^{N} $.Then for $e \in R^{N} $and $‖e‖ $ sufficiently small ...

Question

Theorem:

Let $f$ be twice continuously differentiable in a neighborhood of a point $ x^{∗} \in R^{N} $. Then for $e \in R^{N} $and $‖e‖ $ sufficiently small $$ f(x^{*}+ e) = f(x^{*})+ \nabla{f(x^{*})^{T}e} + e^{T}\nabla^{2}f(x^{*})e/2 + o(||e||^{2}). $$

I need explanation about this theorem. How I should prove them? Maybe you have simple steps.