Consider the following equation. f(x, ) = yəlx, P(1, 2), u = }(21 + V5i) (a)...
Consider the following. f(x, y, z) = xe3yz, P(2,0,1), u } (a) Find the gradient of f. Vf(x, y, z) = (b) Evaluate the gradient at the point P. VF(2,0, 1) = (c) Find the rate of change of fat P in the direction of the vector u. Duf(2, 0, 1) =
please circle the answer! (1 point) Suppose f (x, y) = , P = (1, 3) and v 3i - 2j A. Find the gradient of f Vf = i+ j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (Vf) (P) it j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf...
1 1 Consider the function f(x.y,z) 2x y 2 the point P(3,0,1), and the unit vector u 0 Compute the gradient of f and evaluate it at P b. Find the unit vector in the direction of maximum increase of f at P c. Find the rate of change of the function in the direction of maximum increase at P d. Find the directional derivative at P in the direction of the given vector. a. 1 1 Consider the function...
(1 point) Suppose f (r,y)= P = (1, -2) and v=3i - 3j. A. Find the gradient of 1 Uf = 1 it -x/y^2 Note: Your answers should be expressions of x and y, eg "3x - 4y" j j B. Find the gradient off at the point P. (VA)(P) = 1 i+ -2 Note: Your answers should be numbers C. Find the directional derivative off at P in the direction of v. Duf = 9 Note: Your answer should...
4. Let 3 f(x, y, z) = x’yz-xyz3, 4 P(2, -1, 1), u =< 0, > 5 a). Find the gradient of f. b). Evaluate the gradient at the point P. c). Find the rate of change of f at the point of P in the direction of the vector u.
(6 points) Are the following statements true or false? 1. fi (a, b) is parallel to u 2.If iü is a unit vector, then fila, b) is a vector ? 3. Suppose f(a, b) and f(a, b) both exist. Then there is always a direction in which the rate of change of f at (a, b) is zero ?4.I f(x, y) has f. (a, b) 0 and f,(a, b) 0at the point (a, b), then f is constant everywhere |...
For the function f(x,y,z)==xyz and the point P=(-1, 8, 2): a) Calculate the gradient at P. Vf(-1, 8, 2) = b) Find the rate of change in the direction v=(2, 2, - 1) at P. D.f(-1, 8, 2)= c) Find the maximum rate of change of f at P. MAX RATE OF CHANGE =
2. Let f(x, y) = xy (2] (a) Findäf af and Vf. 5 (b) Find a unit vector u for which Duf(v2, V2) = 0. 2. Let f(x, y) = xy (2] (a) Findäf af and Vf. 5 (b) Find a unit vector u for which Duf(v2, V2) = 0.
(1 point) Letf(x,y) = xer'-y and P = (8, 64). (a) Calculate lIVf(P)lI. (b) Find the rate of change of f in the direction Vf(P) (e) Find the rate of change of f in the direction of a vector making an angle of 4 5 with Vf(P). Answers (a) 129.25
3. Given: f(x, y) = x3y2. Find: a) Duf(x, y) in the direction of (2, -1) at the point (1, 2, 4). b) Vf at the point (1, 2, 4). c) Find the maximum slope at (1, 2, 4).