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Consider the function g defined by g(r, y) = cos (Tx V) + COS log3(r – y) Do as indicated. 1. Determine 2. Calculate thc instantancous rate of change of g at the point (4, 1, 2) in the direction of the vector v = (1,2). 3. In what direction does g have the maximum directional derivative at (r, y) = (4, 1)? %3D What is the mnaximum directional derivativec?

Consider the function g defined by g(r, y) = cos (Tx V) + COS log3(r – y) Do as indicated. 1. Determine 2. Calculate thc instantancous rate of change of g at the point (4, 1, 2) in the direction of the vector v = (1,2). 3. In what direction does g have the maximum directional derivative at (r, y) = (4, 1)? %3D What is the mnaximum directional derivativec?

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 g defined by 1 g(r, y) = cos (Tx T) + log3(r – y) Do as indicated. 1. Determine dyðr 2. Calculate the instantancous rate of change of g at the point (4, 1,2) in the direction of the vector v = (1, 2). 3. In what direction does g have the maximum directional derivative at (r, y) = (4, 1)? %3D What is the mnaximum directional derivative?
Transcribed Image Text:Consider the function g defined by 1 g(r, y) = cos (Tx T) + log3(r – y) Do as indicated. 1. Determine dyðr 2. Calculate the instantancous rate of change of g at the point (4, 1,2) in the direction of the vector v = (1, 2). 3. In what direction does g have the maximum directional derivative at (r, y) = (4, 1)? %3D What is the mnaximum directional derivative?
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In substituting the point (4,1,2) in the partial derivatives, why does the terms without x and y becomes zero?

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Follow-up Question

Why did these become zero?

From part U), Be (4.1,2) -7 Ī sinl4x) (4-1) Inca) ( log (33)² 3 ln(3) 3dn(3) A(4) sin (4*) + 2 JT 3 dn13) (log(3))" (4P12) 3 dn (8) 3 In (3)
Transcribed Image Text:From part U), Be (4.1,2) -7 Ī sinl4x) (4-1) Inca) ( log (33)² 3 ln(3) 3dn(3) A(4) sin (4*) + 2 JT 3 dn13) (log(3))" (4P12) 3 dn (8) 3 In (3)
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