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(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that...

(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that H(x, y) ≥ 0 for all (x, y). Hint: find the minimum value of H.

(4) Let f(x, y) = (y − x^2 ) (y − 2x^2 ). Show that the origin is a critical point for f which is a saddle point, even though on any line through the origin, f has a local minimum at (0, 0)

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