Consider the function g defined by 1 g(x, y) = sin (TVry) + log3(x – 3y) Do as indicated. 1. Determine dydx 2. Calculate the instantaneous rate of change of g at the point (4, 1,0) 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 minimum directional derivative?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the function g defined by
1
g(x, y) = sin (7 vVay) +
log3(x – 3y)
Зу)
Do as indicated.
1. Determine
dydx"
2. Calculate the instantaneous rate of change of g at the point (4, 1,0) 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 minimum directional derivative?
Transcribed Image Text:Consider the function g defined by 1 g(x, y) = sin (7 vVay) + log3(x – 3y) Зу) Do as indicated. 1. Determine dydx" 2. Calculate the instantaneous rate of change of g at the point (4, 1,0) 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 minimum directional derivative?
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