What can we say about $f(\boldsymbol{x})$ if $(\nabla f (\boldsymbol{x}))\cdot \boldsymbol{x}=f(\boldsymbol{x})$? Here $\boldsymbol{x} \in \mathbb{R}^2$. I guess it's a cone, but how to show it? Thanks a lot!
2026-04-06 14:42:08.1775486528
What can we say about $f(\boldsymbol{x})$ if $\nabla f (\boldsymbol{x})\cdot \boldsymbol{x}=f(\boldsymbol{x})$?
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