Norm of $||(x-x^*,y-y^*,z-z^*) ||\leq ||\nabla J(x,y,z)||$

I want to prove that

$ $ ||(x-x^*,y-y^*,z-z^*) ||\leq ||\nabla J(x,y,z)||,$ $

where $ J(x,y,z)=\exp(\frac{x+y+z}{2016})+\frac{x^2+2y^2+3z^2}{2}$ and $ (x^*,y^*,z^*)$ is the minimum of $ J$ .

Also, I have $ $ ||(x-x^*,y-y^*,z-z^*) ||^2\leq U^t H U$ $ with $ H$ the Hessian matrix of $ J$ and $ $ U=(x-x^*,y-y^*,z-z^*).$ $

Could you give me some clue to complete the proof?

Thanks!