Let f (x, y) = ln sqrt{ x^2 + y^2} a. Find the directional derivative of f at the point (3,4) in the direction of v = <−1,1>. b. Find the direction in which f increases most rapidly (at (3, 4)), and the maximum value of f at (3, 4).
Let f (x, y) = ln sqrt{ x^2 + y^2} a. Find the directional derivative of f at the point (3,4) in the direction of v = <−1,1>. b. Find the direction in which f increases most rapidly (at (3, 4)), and the maximum value of f at (3, 4).
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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Let f (x, y) = ln sqrt{ x^2 + y^2}
a. Find the directional derivative of f at the point (3,4) in the direction of v = <−1,1>.
b. Find the direction in which f increases most rapidly (at (3, 4)), and the maximum value of f at (3, 4).
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