A quick question about the Hessian matrix

A function $f$ that has continuous third order partial derivatives in $\mathbb{R}^n$. I'm just wondering that since the partial derivatives are continuous then the Hessian matrix is symmetric. Is that correct?

Thanks.

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Yes. If the third order partials are continuous, then the second order partials are and so Clairaut's theorem applies -- mixed partials are equal and thus the Hessian is symmetric. – Bill Cook Mar 19 '12 at 18:13
Thank you! Very helpful. – docjay Mar 19 '12 at 18:15
Yes, that is correct. You only need second order partials to be continuous. See en.wikipedia.org/wiki/Symmetry_of_second_derivatives – Robert Israel Mar 19 '12 at 18:15