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Find the maximum rate of change of f at the given point and the direction in...
(1 point) Find the maximum rate of change of f(x,y) = ln(x2 + y²) at the point (-2,-5) and the direction in which it occurs. Maximum rate of change: Direction (unit vector) in which it occurs:
3. Find the maximum rate of change of f(x, y) = e-ry at (1, 1) and the direction in which it occurs. 4. Given (x + y)2 + sin(x + y) = y, use the Implicit Function Theorem to find out
Find the square of the maximum rate of change of f (, y) = xy + 2 (x) at the point (4,6), wherer (2) =42. The square of the maximum rate of change of the function is
Stuck on this problemGiven the functionf(x,y)=ln(2x2+3y2)a) Find the directional derivative at (1,2) in the directionv=2i+3jb) Find the maximum rate of change and of f at the given pointand the direction at which it occurs.
(1 point) Consider the function f (x, y) = 3x2 + 4y2. f at the point (-4,1) in the direction given by Find the the directional derivative of the angle 0 Find the vector which describes the direction in which f is increasing most rapidly at (-4, 1)
(1 point) Consider the function f (x, y) = 3x2 + 4y2. f at the point (-4,1) in the direction given by Find the the directional derivative of the angle 0 Find...
(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...
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)...
8) a) About how much will f(x,y,z) = xy?z? change if the point (x,y,z) moves from (3.-7.-6) a distance of ds = 0.5 units in the direction of 21 +27 - K? b) Find the maximum change in f(x,y,z) in moving 0.5 units away in any direction, and indicated in what direction this occurs.
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(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