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!