Consider the function F(x,y) = e-x²12-y²/2 and the point P(2,-2). a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find a vector that points in a direction of no change in the function at P. a. The direction of steepest ascent is The direction of steepest descent is b. Which of the following vectors points in a direction of no change of the function at P(2,-2)? O A. (1,1) B. (0,1) OC. (1,0) OD. (1,1)
Consider the function F(x,y) = e-x²12-y²/2 and the point P(2,-2). a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find a vector that points in a direction of no change in the function at P. a. The direction of steepest ascent is The direction of steepest descent is b. Which of the following vectors points in a direction of no change of the function at P(2,-2)? O A. (1,1) B. (0,1) OC. (1,0) OD. (1,1)
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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Transcribed Image Text:**Consider the function** \( F(x,y) = e^{-x^2/2 - y^2/2} \) **and the point** \( P(2, -2) \).
**a.** Find the unit vectors that give the direction of steepest ascent and steepest descent at \( P \).
**b.** Find a vector that points in a direction of no change in the function at \( P \).
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**a.** The direction of steepest ascent is \( \left( \, \Box, \Box \, \right) \).
The direction of steepest descent is \( \left( \, \Box, \Box \, \right) \).
**b.** Which of the following vectors points in a direction of no change of the function at \( P(2, -2) \)?
- \( \text{A. } (-1, 1) \)
- \( \text{B. } (0, 1) \)
- \( \text{C. } (1, 0) \)
- \( \text{D. } (1, 1) \)
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