In the following several gradients and Hessian matrices are given. Classify them based on the extremal lines they identify. Here are the classification rules as a reminder Ridge lines Valley lines grad f(x,y) | €2 21<0 grad f(x, y)||c 0<12 -2y2 -1 0 H= 0 Valley Line ;gradf 1 3 0 H = 0 -5y4 2 gradf = 3 Valley Line -2y2 1 0 H = ;gradf = 0 Not an Extremal Line [8] -2y2 -1 0 H = ;gradf = 0 [A] Ridge Line 0 H == ;gradf = 0 -5y2-6, Not an Extremal Line 3 0 H = ;gradf = 0 5y2+4] Not an Extremal Line []
In the following several gradients and Hessian matrices are given. Classify them based on the extremal lines they identify. Here are the classification rules as a reminder Ridge lines Valley lines grad f(x,y) | €2 21<0 grad f(x, y)||c 0<12 -2y2 -1 0 H= 0 Valley Line ;gradf 1 3 0 H = 0 -5y4 2 gradf = 3 Valley Line -2y2 1 0 H = ;gradf = 0 Not an Extremal Line [8] -2y2 -1 0 H = ;gradf = 0 [A] Ridge Line 0 H == ;gradf = 0 -5y2-6, Not an Extremal Line 3 0 H = ;gradf = 0 5y2+4] Not an Extremal Line []
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![In the following several gradients and Hessian matrices are given. Classify them based on the extremal lines they identify. Here are the classification rules as a reminder
Ridge lines
Valley lines
grad f(x,y) | €2
21<0
grad f(x, y)||c
0<12
-2y2
-1
0
H=
0
Valley Line
;gradf
1
3
0
H =
0
-5y4
2 gradf
=
3
Valley Line
-2y2
1
0
H =
;gradf
=
0
Not an Extremal Line
[8]
-2y2
-1 0
H =
;gradf
=
0
[A]
Ridge Line
0
H
==
;gradf
=
0 -5y2-6,
Not an Extremal Line
3
0
H
=
;gradf
=
0 5y2+4]
Not an Extremal Line
[]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc38edc4c-494a-4c8f-bcd3-cf23549833c7%2F733addfd-7cf3-406d-9f65-19875765f5b0%2Fzl47dwl_processed.png&w=3840&q=75)
Transcribed Image Text:In the following several gradients and Hessian matrices are given. Classify them based on the extremal lines they identify. Here are the classification rules as a reminder
Ridge lines
Valley lines
grad f(x,y) | €2
21<0
grad f(x, y)||c
0<12
-2y2
-1
0
H=
0
Valley Line
;gradf
1
3
0
H =
0
-5y4
2 gradf
=
3
Valley Line
-2y2
1
0
H =
;gradf
=
0
Not an Extremal Line
[8]
-2y2
-1 0
H =
;gradf
=
0
[A]
Ridge Line
0
H
==
;gradf
=
0 -5y2-6,
Not an Extremal Line
3
0
H
=
;gradf
=
0 5y2+4]
Not an Extremal Line
[]
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