. True or false, 2 pts each. If the statement is ever false, circle false as...

. True or false, 2 pts each. If the statement is ever false, circle false as your answer. No work is required, and no partial credit will be given. In each case, assume f is a smooth function (its derivatives of all orders exist and are continuous).

If f has a constraint g = c, assume that g is smooth and that ∇g is never 0.

(a) If f has a maximum at the point (a, b) subject to the constraint g = c, then we must have f(a, b) ≤ c. TRUE FALSE

(b) If A and B are square matrices and AB is defined, then BA must also be defined. TRUE FALSE

(c) The function f(x, y) = x 2 − 2y has a maximum subject to the constraint x + y = 1. TRUE FALSE

(d) If (x0, y0) is the point where f attains its minimum subject to the constraint g(x, y) = c, then ∇f and ∇g must point in opposite directions at (x0, y0). TRUE FALSE

Expert Solution

Colby Messinger answered 1 year ago

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