Number 27

X 2022-10-13 (1).png . . 190% tion z = f(x, y) and a point P are 23. f ( x, y) = x + 2y - xy- 7x, P = (4, 1) derivative of fin the indicated direc- 24. f(x, y) = xy3 - 2x, P = (1, 1) same functions as in Exercises 7-12. In Exercises 25-28, a function w = F(x, y, z), a vector v and a xy, P = (2, 1) point P are given. of v = (3, 4) (a) Find VF(x, y, z). toward the point Q = (1, -1). (b) Find Dy Fat P, where u is the unit vector in the direction of v. 3 25. F(x, y, z) = 3x 23 + 4xy - 322, V = (1, 1, 1), P = (3, 2, 1) of v = (1, 1). 26. F(x, y, z) = sin(x) cos(y)e' , v = (2, 2, 1), P = (0, 0, 0) toward the point Q = (0, 0). 27. F(x, y, z) = xy - y z2, v= (-1, 7, 3), P = (1,0, -1) P = (1, 1). 2 28. F(x, y, Z) = 2 4 \\2 + 72, V = (1, 1, -2), P = (1, 1, 1) of V = (1, -1). In Exercises 29-30, a function w = F(x, y, z) and a point P are toward the point Q = (-2, -2). give. Find the direction of maximum increase and the maximal value of the directional derivative for F at P = (5, 2) of v = (3, 1) . 29. F(x, y, z) = x2 + y2 - z2 + xyz at P = (2, 1, 3) 1 toward thanAint n - ( 7 7) 30 F( x v 7) = at P = (1 0 1) 720 F DEV 5:51 PM 5 Partly sunny O 10/13/2022