MATH V1207 Midterm: MATH V1205 Columbia Spring01Mid1Ans

• School: Columbia University
• Department: Mathematics
• Course: MATH V1207
• Professor: All

Document Summary

Midterm examination #1 answers: february 14, 2001: a ladybug is hovering at the point (x, y, z) = (0, 1, 2). The temperature is given by the function f (x, y, z) = zexy: the temperature increases most rapidly in the direction of f = hyzexy, xzexy, exyi. So the direction is h2, 0, 1i with rate | f| = 5. 2 , 0, 1i without changing temperature: suppose f (x, y) = 2x2 + 3y2 4x 5, since fx = 4x 4 and fy = 6y, the critical point for f (x, y) is (1, 0). Note that f (1, 0) = 7: use the method of lagrange multipliers to nd the absolute maximum and minimum of f (x, y) on the region x2 + y2 16. If g(x, y) = x2 + y2, then f = g implies that 4x 4 = 2x and.