Question

Consider the following. f(x, y, z) = xe5yz, P(1, 0, 2), u=1/3,-2/3,2/3. (a) Find the gradient...

Consider the following. f(x, y, z) = xe5yz, P(1, 0, 2), u=1/3,-2/3,2/3. (a) Find the gradient of f. ∇f(x, y, z) = (b) Evaluate the gradient at the point P. ∇f(1, 0, 2) = (c) Find the rate of change of f at P in the direction of the vector u. Duf(1, 0, 2) =

Homework Answers

Answer #1

Please thumbs up if it was helpful will be glad to know :)

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
f(x, y, z) = xe4yz, P(1, 0, 3), u = <2/3, -1/3, 2/3> (a) Find the...
f(x, y, z) = xe4yz, P(1, 0, 3), u = <2/3, -1/3, 2/3> (a) Find the gradient of f. ∇f(x, y, z) = <   ,   ,   > (b) Evaluate the gradient at the point P. ∇f(1, 0, 3) = <   ,   ,   > (c) Find the rate of change of f at P in the direction of the vector u. Duf(1, 0, 3) =
Consider the following. f(x, y) = x/y,    P(4, 1),    u = 3 5  i + 4 5  j...
Consider the following. f(x, y) = x/y,    P(4, 1),    u = 3 5  i + 4 5  j (a) Find the gradient of f. (b) Evaluate the gradient at the point P. (c) Find the rate of change of f at P in the direction of the vector u.
In the following functions: a) Find the gradient of f. , b) Evaluate the gradient at...
In the following functions: a) Find the gradient of f. , b) Evaluate the gradient at point P. and c) Find the rate of change of f in P, in the direction of vector. 1- f(x. y) = 5xy^2 - 4x^3y, P( I , 2), u = ( 5/13, 12/13 ) 2- f(x, y, z) = xe^2yz , P(3, 0, 2), u = (2/3, -2/3, 1/3)
Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and ?=3?+2?v=3i+2j. A. Find the gradient of f. ∇?=∇f=  ?+i+  ?j Note: Your answers should...
Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and ?=3?+2?v=3i+2j. A. Find the gradient of f. ∇?=∇f=  ?+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. (∇?)(?)=(∇f)(P)=  ?+i+  ?j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of ?v. ???=Duf= D. Find the maximum rate of change of f at P. E. Find the (unit) direction vector in which the maximum rate...
Let f(x, y) = x^2 ln(x^3 + y). (a) Find the gradient of f. (b) Find...
Let f(x, y) = x^2 ln(x^3 + y). (a) Find the gradient of f. (b) Find the direction in which the function decreases most rapidly at the point P(2, 1). (Give the direction as a unit vector.) (c) Find the directions of zero change of f at the point P(2, 1). (Give both directions as a unit vector.)
For f(x,y,z) = sqrt(35-x^2-4y^2-2z) 1. Find the gradient of f(x,y,z) 2. Evaluate delta f(x,y,z) 3. Find...
For f(x,y,z) = sqrt(35-x^2-4y^2-2z) 1. Find the gradient of f(x,y,z) 2. Evaluate delta f(x,y,z) 3. Find the unit vectors U+ and U- , that give the direction of steepest ascent and the steepest descent respectively.
Consider the function F(x, y, z) =x2/2− y3/3 + z6/6 − 1. (a) Find the gradient...
Consider the function F(x, y, z) =x2/2− y3/3 + z6/6 − 1. (a) Find the gradient vector ∇F. (b) Find a scalar equation and a vector parametric form for the tangent plane to the surface F(x, y, z) = 0 at the point (1, −1, 1). (c) Let x = s + t, y = st and z = et^2 . Use the multivariable chain rule to find ∂F/∂s . Write your answer in terms of s and t.
let f(x,y) = 2xy+4y^2 a) find the rate of change f at the point P(3,2) in...
let f(x,y) = 2xy+4y^2 a) find the rate of change f at the point P(3,2) in the direction of u= [1,3] b) in what direction does f have the maximum rate of change? what is the maximum rate id change?
Consider the surface defined by z = f(x,y) = x+y^2+1. a)Sketch axes that cover the region...
Consider the surface defined by z = f(x,y) = x+y^2+1. a)Sketch axes that cover the region -2<=x<=2 and -2<=y<=2.On the axes , draw and clearly label the contours for the eights z=0 ,z=1,and z=2. b)evaluate the gradients of f(x,y) at the point (x,y) = (0.-1), and draw the gradient vector on the contour diagrqam . c)compute the directional derivative at(x,y) = (0,-1) in the direction V =<2,1>.
] Consider the function f : R 2 → R defined by f(x, y) = x...
] Consider the function f : R 2 → R defined by f(x, y) = x ln(x + 2y). (a) Find the gradient of f(x, y) at the point P(e/3, e/3). (b) Use the gradient to find the directional derivative of f at P(e/3, e/3) in the direction of the vector ~u = h−4, 3i. (c) Find a unit vector (based at P) pointing in the direction in which f increases most rapidly at P.