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Consider the function Question 1 x f(x, y) = -y ln x + x lny + y a) Find the directional derivative of f at the point (1, 2) in the direction of the vector v = (-√√3, -1). b) In which direction does f have the maximum rate of change, and what is this maximum rate of change?

Consider the function Question 1 x f(x, y) = -y ln x + x lny + y a) Find the directional derivative of f at the point (1, 2) in the direction of the vector v = (-√√3, -1). b) In which direction does f have the maximum rate of change, and what is this maximum rate of change?

Advanced Engineering Mathematics
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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Consider the function Question 1 f(x, y) = -y ln x + xlny+ y a) Find the directional derivative of f at the point (1, 2) in the direction of the vector v = (-√√3,-1). b) In which direction does f have the maximum rate of change, and what is this maximum rate of change?
Transcribed Image Text:Consider the function Question 1 f(x, y) = -y ln x + xlny+ y a) Find the directional derivative of f at the point (1, 2) in the direction of the vector v = (-√√3,-1). b) In which direction does f have the maximum rate of change, and what is this maximum rate of change?
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