Let f be: R²→R given by f(x,y) = (y - x²) (y – 2x²) Show that f has no local minimum at (0,0), but that every restriction flg

Question

Let f be: R²→R given by f(x,y) = (y - x²) (y – 2x²)
Show that f has no local minimum at (0,0), but that every restriction flg for every line G⊂R² through the origin, has a local minimum at (0,0).

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