Question

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

0 0
Add a comment Improve this question Transcribed image text
Answer #1

Given theit, t(X,Y,Z) = Lxyz , P = (-4, 8, 2) 2 goudt FA P ( E & 2 ) ( 7 th + dx be - 54972) +1(302)1, 1973 y 1 + x2 3 + xy V14. 7 = (8) - ] - 4R ). ( 29 +27 - R 1 (-1,82) N 4+4+ 16-2-4 3 > Vf. 10 3. (-1,8, 2) D+/-1, 8, 2) 10 3 ars © since Now we fin

Add a comment
Know the answer?
Add Answer to:
For the function f(x,y,z)==xyz and the point P=(-1, 8, 2): a) Calculate the gradient at P....
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • Consider the following. f(x, y, z) = xe3yz, P(2,0,1), u } (a) Find the gradient of...

    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)...

    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...

    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...

  • 17. Given f(x, y, z) = x^yz -- xyz', P(2,-1,1) and vector v =<1,0,1 >. Find...

    17. Given f(x, y, z) = x^yz -- xyz', P(2,-1,1) and vector v =<1,0,1 >. Find i. the directional derivative of the function at the point P in the direction of v. ii. the maximum rate of change of f.

  • (1 point) Suppose f (r,y)= P = (1, -2) and v=3i - 3j. A. Find the...

    (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...

  • Let g(x, y, z) = x2 + xy + xyz?. (a) Find the gradient of g....

    Let g(x, y, z) = x2 + xy + xyz?. (a) Find the gradient of g. (b) Find the rate of change of g at the point (1,-1,2) in the direction of the vector v = (8,4,-1).

  • (1 point) Letf(x,y) = xer'-y and P = (8, 64). (a) Calculate lIVf(P)lI. (b) Find the...

    (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

  • Use the gradient rules to find the gradient of the given function, f(x,y,z) = x+yz y+xz...

    Use the gradient rules to find the gradient of the given function, f(x,y,z) = x+yz y+xz Choose the correct answer below. 1 O A. Vf(x,y,z) = -((1-z?)z(z2 - 1).y? - x?) (y + xz)? OB. Vf(x,y,z) = (z(1-z?)y(z? - 1),z2 + x2) (x + yz)? O c. Vf(x,y,z) = (y(1+z2),x(z? + 1).y? - z?) (x + yz)? OD. Vf(x,y,z) = -(y (1-2²), x(2² - 1), y² - x²) (y + xz)2

  • Question 8 Let f(x, y) = ln(x + 2y). What is the maximum rate of change...

    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)

  • Consider the following equation. f(x, ) = yəlx, P(1, 2), u = }(21 + V5i) (a)...

    Consider the following equation. f(x, ) = yəlx, P(1, 2), u = }(21 + V5i) (a) Find the gradient of f. Vf(x, y) = (b) Evaluate the gradient at the point P. Vf(1, 2) = (c) Find the rate of change of fat P in the direction of the vector u. Duf(1, 2) =

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT