MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS ASSIGNMENT 9 (OPTIONAL) MATH 1005 DIM: D4:C*:M SR 4 1. Find the point P on the parabola y = 3:2 that is closest to (%}0). -2- 2. A rectangle has side lengths a, b which sum to 5. What is the maximum area of such a rectangle?3. An engineer wants to create a rectangular path with one side costing l4 SIS/meter and the other three costing 3 SIS/meter. If they must enclose 19 square meters, what dimensions should they choose to minimize cost? -5- (c) f(x) = 10y* + 3x3 +8xy. (d) f(x) = -2(x2 +y? )el-42).-6- 5. Use a tree diagram to write out the chain rule for the following cases. (a) w = f(x, y, z) where x = x(u, v), y = y(u), and z = z(u, v) (b) R = f (t), where t = g(w, x, y, z). -8 - (c) z = vxe(2xy), x =6st - 9,y = 4+# 7. Find the local minimum, maximum, and saddle points of the following (a) f(x,y) = -10x2 +8xy -9y2 -10x -6y