please solve now (a) 3 marks The directional derivative of f(x,y) at a point P in...
s (ls points) 1/ Given f(x,>)-xy+e" sin y and P(1,0) a) Find the directional derivative of fat P in the direction of Q(2, 5). b) Find the directions in which the function increases and decreases most rapidly atP e) Find the maximum value of the directional derivative of fat P. d) Is there a direction u in which the directional derivative o f fat P equals 1? If there is, find u. If there is no such direction, explain. e)...
6. For a given function f(x, y), is noted that at the point P(1,1) the directional derivative in the direction towards (0,0) is 1, while the directional derivative towards (1.2) is -1. Find andf at 6. For a given function f(x, y), is noted that at the point P(1,1) the directional derivative in the direction towards (0,0) is 1, while the directional derivative towards (1.2) is -1. Find andf at
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...
Find the directional derivative of the function f(x,y,z) = z4−x3y2 at P(1,-1,1) in the direction of the vector from P(1,-1,1) to the point Q(2,1,0). What is the maximum rate of change of f at the point P(1,-1,1) and in which direction
Find the directional derivative D−→ u f(x,y) of the function f(x,y) = x2 + 3xy + y3 where →− u is the unit vector given by angle θ = π 4. What is D−→ u f(1,1)?
3 U + tyy = 0. 3. Find the directional derivative of f(x,y) 2In y at the point P(2,1) in the direction ū= 21+ 4. Find the linearization of f(x,y) = x2 + y2 at the point P(3, 4) and use it to
Find the directional derivative of f(x,y,z)=xy+z^3 at the point (2,3,1) in the direction of a vector making an angle of 3π/4 with ∇f(2,3,1).
Find the directional derivative off at P in the direction of the vector U f(x,y,z) = x²lny P(5,1); U = wait à 1 = ( )
(1 point) Use the contour diagram for f(x, y) shown below to estimate the directional derivative off in the direction v at the point P. (a) At the point P = (2, 2) in the direction ✓ = 7, the directional derivative is approximately O‘ot 16.0 18.0 12.0 14.0 2.0 (b) At the point P = (3, 2) in the direction ✓ = -1, the directional derivative is approximately 8.0 (c) At the point P = (4,1) in the direction...
3. Find the gradient ãf and the directional derivative at the point P(1,-1,2) in the direction a = (2,-1,1) for the function f(x, y, z) = xºz-yx + 2. In which direction is the directional derivative at P decreasing most rapidly and what is its value?