If $f:\mathbb{R}^2 \rightarrow \mathbb{R}, f(x,y) = (y-x^2)(y-2x^2)$, then $(0,0)$ is a min. point of $f$ restricted to any line through origin.
Why is $(0, 0)$ not a minimum of $f(x, y) = (y-3x^2)(y-x^2)$?