Can anyone help me understand the following formula? Is there a way to think about this geometrically?
$$\nabla f(x+p) = \nabla f(x) + \int_0^{1}\nabla^2f(x+tp)pdt$$ where t is between 0 and 1.
Note: $f:R^n \rightarrow R$. So x and p in the equation are $R^n$ vectors.