MTH 241 Final: Math 241 Final Exam V2
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Then neatly sketch and label the path between t = 0 and t = 6 : (10 points) let f(x, y, z) = (xyz, x sin(y), yz). Calculate divf and curlf: (15 points, w = x2 + y2, x = s cos(t), y = s sin(t). S at the point where t = /3 and s = 2: z = x2 cos(xy). Show the global minimum of f (x, y) is 0, i. e. f (x, y) 0. (hint: there will be an entire ray of critical points) Use the result above to prove the arithmetic/geometric mean inequality: 2: (15 points) find the absolute maximum and minimum values of f (x, y) = F(x, y, z) = (y + z, x + 2y, sin(z) + x: find a potential function f (x, y, z), let c be the curve parameterized. , t2 t + 1) for 0 t 3.
