Question

Let f(x, y) = xe^{x^2-y} and P = (8, 64). (a) Calculate ||?f_P||. (b) Find the rate of change of f in the direction ?f_P. (c) Find the rate of change of f in the direction of a vector making an angle of 45° with ?f_P. Answers : (a) (b) (c)

Name: Let f(x, y) = xe^x^2-y and P = (8, 64). (a) Calculate ||?fP||. (b) Find the rate of change of f in the direction ?fP. (c) Find the rate of change of f in the direction of a vector making an angle of 45° with ?fP. Answers : (a) (b) (c)
Uploaded: 2019-07-25T16:52:03-08:00
Duration: 1 min 10 s
Channel: Fuzail Shakir
Description: Let f(x, y) = xe^x^2-y and P = (8, 64). (a) Calculate ||?fP||. (b) Find the rate of change of f in the direction ?fP. (c) Find the rate of change of f in the direction of a vector making an angle of 45° with ?fP. Answers : (a) (b) (c)

          Let f(x, y) = xe^{x^2-y} and P = (8, 64). (a) Calculate ||?f_P||. (b) Find the rate of change of f in the direction ?f_P. (c) Find the rate of change of f in the direction of a vector making an angle of 45° with ?f_P. Answers : (a) (b) (c)

Let f(x, y) = xe^x^2-y and P = (8, 64). (a) Calculate ||?fP||. (b) Find the rate of change of f in the direction ?fP. (c) Find the rate of change of f in the direction of a vector making an angle of 45° with ?fP. Answers : (a) (b) (c)

Added by Jeremy P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Fuzail Shakir

07/25/2019

Step 1

To do this, we'll find the partial derivatives with respect to x and y: ∂f/∂x = e^(-y) ∂f/∂y = -x * e^(-y) Now, we can evaluate the gradient at point P = (8, 64): ∇f(P) = (e^(-64), -8 * e^(-64)) (a) Show more…

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Let f(x, y) = x*e^(x^2-y) and P = (8, 64). (a) Calculate ||grad f_P||. (b) Find the rate of change of f in the direction grad f_P. (c) Find the rate of change of f in the direction of a vector making an angle of 45 degrees with grad f_P.