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  3. . true or false, 2 pts each. if the statement is e

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

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Advance Math

. True or false, 2 pts each. If the statement is ever false,circle false as your answer. No work is required, and no partialcredit 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 ?gis never 0.

(a) If f has a maximum at the point (a, b) subject to theconstraint 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 BAmust also be defined. TRUE FALSE

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

(d) If (x0, y0) is the point where f attains its minimum subjectto the constraint g(x, y) = c, then ?f and ?g must point inopposite directions at (x0, y0). TRUE FALSE

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