# Multivariable unconstrained optimization

I was just wondering how to answer this kind of question:

How do I answer this question using concepts such as stationary point, directional derivative, and linear independence?

Brief outline: The vectors (1, 1) and (1, -1) are linearly independent in $\mathbb{R}^2$, then the gradient of $f$ at $x^*$ is equal to $0$, and hence $x^*$ is a stationary point of $f$. Try and fill in the details yourself!
• The gradient of $f$ at $x^*$ is zero, which you should be able to prove using ideas from multivariable calculus – B. Mehta Sep 23 '17 at 17:57