Consider the function g defined by 1 g(x, y) = cos (TaV) + log3 (r-y) Do as indicated. 1. Determine dydx 2. Calculate the instantaneous 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 (x, y) = (4,1)? What is the maximum directional derivative?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 17E: Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.
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Consider the function g defined by
1
g(x, y) = cos (TI /T)+
log3 (x - y)
Do as indicated.
1. Determine
2. Calculate the instantaneous 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 (x, y) = (4, 1)?
What is the maximum directional derivative?
Transcribed Image Text:Consider the function g defined by 1 g(x, y) = cos (TI /T)+ log3 (x - y) Do as indicated. 1. Determine 2. Calculate the instantaneous 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 (x, y) = (4, 1)? What is the maximum directional derivative?
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