Let F = (6xyz + 2sinx, 3x^2z, 3x^2y). Find a function f so that F = \bigtriangledown f , and f(0, 0, 0) = 0 .
Find the point(s) on the surface z^2 = xy + 1 which are closest to the point (7, 8, 0).
Show a separate graph of the constraint lines and the solutions that satisfy each of the following constraints: a. 3A + 2B ? 18 b. 12A + 8B ? 480 c. 5A + 10B = 200
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