9. Let f(x, y) = x² - 5xy a. Find the gradient of f(x, y) b. Find the directional derivative at (2,1) in the direction of = −i + 3j c. Find the equation of the tangent line on f(x, y) at (2,1) - hint: the coefficient on the x should be 1 d. Find the linearization L(x, y) off at (2,1) e. Use the linearization to approximate f(1.9,.9)
9. Let f(x, y) = x² - 5xy a. Find the gradient of f(x, y) b. Find the directional derivative at (2,1) in the direction of = −i + 3j c. Find the equation of the tangent line on f(x, y) at (2,1) - hint: the coefficient on the x should be 1 d. Find the linearization L(x, y) off at (2,1) e. Use the linearization to approximate f(1.9,.9)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
Transcribed Image Text:9. Let f(x, y) = x² — 5xy
a. Find the gradient of f(x, y)
b. Find the directional derivative at (2,1) in the direction of = −i + 3j
c. Find the equation of the tangent line on ƒ (x, y) at (2,1)
hint: the coefficient on the x should be 1
d. Find the linearization L(x, y) off at (2,1)
e. Use the linearization to approximate f(1.9,.9)
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