# Lagrange remainder for multivariate Taylor expansion?

Assume that $f:R^n\to R$ is an analytic function and we want to use the 2nd order Taylor expansion around, let say 0. Is it correct to write the remainder in the Lagrange form? I.e. $f(X) = f(0) + \nabla f(0) X^T + \frac{1}{2}X H(hX)X^T,$
where $H(X)$ is the hessian of $f$ and for a $0<h<1$.

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