(1 point) Find the maximum rate of change of f(x,y) = ln(x2 + y²) at the...
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 5 sin(xy), (0,8) maximum rate of change direction vector
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
3) Suppose that w = f(x, y, z) = ln(x y2z3). a) (20 pts.) Find the unit vector in the direction of most rapid increase in w at the point (x,y,z) = (1,-2,-3) b) (15 pts.) Find the rate of change in w in this direction at (1,-2,-3).
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...
Question 8 Let f(x, y) = ln(x + 2y). What is the maximum rate of change of fat P(1,0)? Formulas: The maximum rate of change of f at P(20, yo) is | Vf(x0,yo) = V(fx (30, yo))2 + (fy(20, yo))? The gradient of fis f(x,y) = (fa(z,y), fy (z,y)) and substitute * = 0, y = yo into V f(a,y) to get f(go,yo) of f at the point P(0.yo)
(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...
a) A concentration of a carbon monoxide in a tank is described by f(X,y,z) X2 + y2 + Z2. Based on Fick's Law, the diffusion happens in the direction of maximum decrease of concentration Point P is at (1, -2, 3) in the respective tank. Find a vector field to describe diffusion field that happens in the tank. 1. Determine a unit vector in the direction of diffusion at P. ii. Determine unit vector(s) in the direction of zero change...
1. Let f(x,y) = (2-7-% and g(x,y) = v f(x,y). J(1)(4 points) Find the maximum value of g(y). |(272 points) At which point(s) (x,y) and in the direction of which unit vector(s) ů does the maximum value for the directional derivative Dif(x,y) occur?
7. Find the maximum and minimum rate and direction for f(x, y, z) = 2-2 + y ln x at (3, 4, 5)
Let f(x, y, z) = xeyz – cos(x2 – y2 + 22) a) Find the directional derivative of f at the point (0,0,0) toward the point (1,2,0). b) Find the maximum rate of change of f at point (0,0,0). In which direction does the max rate of change at (0,0,0) does occur? (two questions here!)