Mean value theorem (multivariate case)

If $f: \mathbb{R}^n \rightarrow \mathbb{R}$ is twice continuously differentiable, we have that:
$\nabla f(x+p) = \nabla f(x) + \int_{0}^1 \nabla^2 f(x+tp) p dt$
for some $t \in (0,1)$ and $p \in \mathbb{R}^n$