2. For the function z = f(x, y) is known f(2, -1) = -2, f.(2, –1) = -1, f,(2, –1) = 2. Find the following (a) Gradient of f at the point (2, -1) :grad f(2, -1) (b) Directional derivative of f at the point (2, –1) in the direction of the vector -27+37: fa(2, -1). (c) Estimate f(1.99, –1.02) =
2. For the function z = f(x, y) is known f(2, -1) = -2, f.(2, –1) = -1, f,(2, –1) = 2. Find the following (a) Gradient of f at the point (2, -1) :grad f(2, -1) (b) Directional derivative of f at the point (2, –1) in the direction of the vector -27+37: fa(2, -1). (c) Estimate f(1.99, –1.02) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question

Transcribed Image Text:For the function \( z = f(x, y) \) is known \( f(2, -1) = -2 \), \( f_x(2, -1) = -1 \), \( f_y(2, -1) = 2 \). Find the following:
(a) Gradient of \( f \) at the point \( (2, -1) \) : \( \nabla f(2, -1) \)
(b) Directional derivative of \( f \) at the point \( (2, -1) \) in the direction of the vector \( -2 \hat{i} + 3 \hat{j} \): \( f_{\vec{u}}(2, -1) \).
(c) Estimate \( f(1.99, -1.02) \approx \)
(d) Differential of \( f \) at the point \( (2, -1) \)
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

