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Name(s): Score: Math 148 Lab Assignment 9: §10.5–10.6 Directions: You may work in groups of 2–3 to complete this assignment. Answer each question completely. Show all work to receive full credit, and circle your final answer. 1. Let z = xex/y , where x = cos t and y = e2t . Find dz dt when t = 0. 2. Find the directional derivative of f (x, y) = x2 y 3 −4y at the point (2, −1) in the direction of the vector ~v = h2, 5i. 1 3. Find the gradient of each function. (a) f (x, y) = x3 − 4x2 y + y 2 (b) f (x, y) = p x2 + 2y (c) f (x, y, z) = xeyz + xyez 2 4. Suppose that over a certain region of space the electrical potential V is given by V (x, y, z) = 5x2 − 3xy + xyz. (a) Find the rate of change of the potential at P = (3, 4, 5) in the direction of the vector ~v = h1, 1, −1i. (b) In which direction does V change most rapidly at P ? (c) What is the maximum rate of change at P ? 3 5. Find the local extrema and saddle points of f (x, y) = x4 + y 4 − 4xy + 1. 4