-x²15-y²15 Consider the function F(x,y) = e 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 OA. (1,0) OB. (-1,-1) ⒸC. (1,-1) OD. (0,1) √2√e 4 5 2 e 200 5 √2√e 45 5 8 200 √2√e 4 5 2 e √2√e 2 e 5 +15 00 5 2e b. Which of the following vectors points in a direction of no change of the function at P(-2,2)?

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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-x²15-y²15
Consider the function F(x,y) = e
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
OA. (1,0)
OB. (-1,-1)
ⒸC. (1,-1)
OD. (0,1)
√2√e
4
5
2 e
200
5
√2√e
45
5
8
200
√2√e
4
5
2 e
√2√e
2 e
5
+15
00
5
2e
b. Which of the following vectors points in a direction of no change of the function at P(-2,2)?
Transcribed Image Text:-x²15-y²15 Consider the function F(x,y) = e 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 OA. (1,0) OB. (-1,-1) ⒸC. (1,-1) OD. (0,1) √2√e 4 5 2 e 200 5 √2√e 45 5 8 200 √2√e 4 5 2 e √2√e 2 e 5 +15 00 5 2e b. Which of the following vectors points in a direction of no change of the function at P(-2,2)?
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