The two critical points from the graph of the equations x ′ = − x + y − x 3 , y ′ = − x − y + y 2 and classify the critical point at ( 0 , 0 ) .

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Answer 1

Question

Chapter 11.3, Problem 29E

(a)

To determine

The two critical points from the graph of the equations x′=−x+y−x3, y′=−x−y+y2 and classify the critical point at (0,0).

(b)

To determine

The verification for the critical point (0.881,1.563) to be a saddle point.

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Find the critical point(s) for the function ƒ (x,y) = 6x² − 2x³ + 3y² +6xy Classify each critical point from (a) as the location of a local maximum, local minimum, or saddle point. Support your assertion with an appropriate computation.

Exercise 2: Find and classify the critical points of fx, y=x'+6x'+3y'-12 xy+9x.

Answer 2

Question

Chapter 11.3, Problem 29E

(a)

To determine

The two critical points from the graph of the equations x′=−x+y−x3, y′=−x−y+y2 and classify the critical point at (0,0).

(b)

To determine

The verification for the critical point (0.881,1.563) to be a saddle point.

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Answer 3

Question

Chapter 11.3, Problem 29E

(a)

To determine

The two critical points from the graph of the equations x′=−x+y−x3, y′=−x−y+y2 and classify the critical point at (0,0).

(b)

To determine

The verification for the critical point (0.881,1.563) to be a saddle point.

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Answer 4

Question

Chapter 11.3, Problem 29E

(a)

To determine

The two critical points from the graph of the equations x′=−x+y−x3, y′=−x−y+y2 and classify the critical point at (0,0).

(b)

To determine

The verification for the critical point (0.881,1.563) to be a saddle point.

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Answer 5

Chapter 11.3, Problem 29E

(a)

To determine

The two critical points from the graph of the equations x′=−x+y−x3, y′=−x−y+y2 and classify the critical point at (0,0).

(b)

To determine

The verification for the critical point (0.881,1.563) to be a saddle point.

Answer 6

Chapter 11.3, Problem 29E

(a)

To determine

The two critical points from the graph of the equations x′=−x+y−x3, y′=−x−y+y2 and classify the critical point at (0,0).

Answer 7

Chapter 11.3, Problem 29E

(a)

To determine

The two critical points from the graph of the equations x′=−x+y−x3, y′=−x−y+y2 and classify the critical point at (0,0).

Answer 8

(b)

To determine

The verification for the critical point (0.881,1.563) to be a saddle point.

Answer 9

(b)

To determine

The verification for the critical point (0.881,1.563) to be a saddle point.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

The two critical points from the graph of the equations x ′ = − x + y − x 3 , y ′ = − x − y + y 2 and classify the critical point at ( 0 , 0 ) .

The two critical points from the graph of the equations x′=−x+y−x3, y′=−x−y+y2 and classify the critical point at (0,0).

The verification for the critical point (0.881,1.563) to be a saddle point.

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