Let U = (x, y) in R^2 : x + y le 2. Define f : U to R by f(x, y) = (x - 1)^4 + (y - 2)^4. The minimum value of f over U is

Q37Section ST (Statistics (Q11–Q65))37 of 65

Minimum of quartic over half-plane

Let $U = \{(x, y) \in \mathbb{R}^{2} : x + y \le 2\}$ . Define $f : U \to \mathbb{R}$ by $f(x, y) = (x - 1)^4 + (y - 2)^4$ . The minimum value of $f$ over $U$ is

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