z²+y² 1. Let f(x, y) = xe Answer the following. (a) Compute the direction derivative of f at the point (1, 2), in the direction of (2, 1). Simplify your answer, but do not round! (b) In which direction is the directional derivative of f maximal at the point (0, 2)? Simplify your answer, but do not round! (c) What is the directional derivative of f at (0, 2) in that direction from part (b)? Simplify your answer, but do not round!

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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1² +₂²
1. Let f(x, y) = xe
Answer the following.
ab im
(a) Compute the direction derivative of f at the point (1, 2), in the direction of (2, 1). Simplify your answer,
but do not round!
(b) In which direction is the directional derivative of f maximal at the point (0, 2)? Simplify your answer,
but do not round!
(c) What is the directional derivative of f at (0, 2) in that direction from part (b)? Simplify your answer,
but do not round!
Transcribed Image Text:1² +₂² 1. Let f(x, y) = xe Answer the following. ab im (a) Compute the direction derivative of f at the point (1, 2), in the direction of (2, 1). Simplify your answer, but do not round! (b) In which direction is the directional derivative of f maximal at the point (0, 2)? Simplify your answer, but do not round! (c) What is the directional derivative of f at (0, 2) in that direction from part (b)? Simplify your answer, but do not round!
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