To Prove: The given inequality satisfying the given condition.

Question

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Answer 1

Question

Chapter 14.7, Problem 63E

To determine

To Prove:

The given inequality satisfying the given condition.

To determine

(a)

To Show:

That the set of critical points of the given curve $f (x, y) = α^{- 1} x^{α} + β^{- 1} y^{β} - x y$ is given by $y = x^{α - 1}$ which can be represented in other form as $x = y^{β - 1}$ .

To determine

(b)

To Verify:

The second derivative test gets fail for the given the function at given critical points. Also, for b > 0, the given function is concave up with the given critical point.

To determine

(c)

To Conclude:

The inequality from earlier solution.

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Answer 2

Question

Chapter 14.7, Problem 63E

To determine

To Prove:

The given inequality satisfying the given condition.

To determine

(a)

To Show:

That the set of critical points of the given curve $f (x, y) = α^{- 1} x^{α} + β^{- 1} y^{β} - x y$ is given by $y = x^{α - 1}$ which can be represented in other form as $x = y^{β - 1}$ .

To determine

(b)

To Verify:

The second derivative test gets fail for the given the function at given critical points. Also, for b > 0, the given function is concave up with the given critical point.

To determine

(c)

To Conclude:

The inequality from earlier solution.

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Answer 3

Question

Chapter 14.7, Problem 63E

To determine

To Prove:

The given inequality satisfying the given condition.

To determine

(a)

To Show:

That the set of critical points of the given curve $f (x, y) = α^{- 1} x^{α} + β^{- 1} y^{β} - x y$ is given by $y = x^{α - 1}$ which can be represented in other form as $x = y^{β - 1}$ .

To determine

(b)

To Verify:

The second derivative test gets fail for the given the function at given critical points. Also, for b > 0, the given function is concave up with the given critical point.

To determine

(c)

To Conclude:

The inequality from earlier solution.

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Answer 4

Question

Chapter 14.7, Problem 63E

To determine

To Prove:

The given inequality satisfying the given condition.

To determine

(a)

To Show:

That the set of critical points of the given curve $f (x, y) = α^{- 1} x^{α} + β^{- 1} y^{β} - x y$ is given by $y = x^{α - 1}$ which can be represented in other form as $x = y^{β - 1}$ .

To determine

(b)

To Verify:

The second derivative test gets fail for the given the function at given critical points. Also, for b > 0, the given function is concave up with the given critical point.

To determine

(c)

To Conclude:

The inequality from earlier solution.

Expert Solution & Answer

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Answer 5

Chapter 14.7, Problem 63E

To determine

To Prove:

The given inequality satisfying the given condition.

To determine

(a)

To Show:

That the set of critical points of the given curve $f (x, y) = α^{- 1} x^{α} + β^{- 1} y^{β} - x y$ is given by $y = x^{α - 1}$ which can be represented in other form as $x = y^{β - 1}$ .

To determine

(b)

To Verify:

The second derivative test gets fail for the given the function at given critical points. Also, for b > 0, the given function is concave up with the given critical point.

To determine

(c)

To Conclude:

The inequality from earlier solution.

Answer 6

Chapter 14.7, Problem 63E

To determine

To Prove:

The given inequality satisfying the given condition.

Answer 7

Chapter 14.7, Problem 63E

To determine

To Prove:

The given inequality satisfying the given condition.

Answer 8

To determine

(a)

To Show:

That the set of critical points of the given curve $f (x, y) = α^{- 1} x^{α} + β^{- 1} y^{β} - x y$ is given by $y = x^{α - 1}$ which can be represented in other form as $x = y^{β - 1}$ .

Answer 9

To determine

(a)

To Show:

That the set of critical points of the given curve $f (x, y) = α^{- 1} x^{α} + β^{- 1} y^{β} - x y$ is given by $y = x^{α - 1}$ which can be represented in other form as $x = y^{β - 1}$ .

Answer 10

To determine

(b)

To Verify:

The second derivative test gets fail for the given the function at given critical points. Also, for b > 0, the given function is concave up with the given critical point.

Answer 11

To determine

(b)

To Verify:

The second derivative test gets fail for the given the function at given critical points. Also, for b > 0, the given function is concave up with the given critical point.

Answer 12

To determine

(c)

To Conclude:

The inequality from earlier solution.

Answer 13

To determine

(c)

To Conclude:

The inequality from earlier solution.

Answer 14

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Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

To Prove: The given inequality satisfying the given condition.

To Prove: The given inequality satisfying the given condition.

(a) To Show: That the set of critical points of the given curve f(x,y)=α−1xα+β−1yβ−xy is given by y=xα−1 which can be represented in other form as x=yβ−1.

(b) To Verify: The second derivative test gets fail for the given the function at given critical points. Also, for b > 0, the given function is concave up with the given critical point.

(c) To Conclude: The inequality from earlier solution.

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Chapter 14 Solutions

To Prove:

The given inequality satisfying the given condition.

(a)

To Show:

That the set of critical points of the given curve $f (x, y) = α^{- 1} x^{α} + β^{- 1} y^{β} - x y$ is given by $y = x^{α - 1}$ which can be represented in other form as $x = y^{β - 1}$ .

(b)

To Verify:

The second derivative test gets fail for the given the function at given critical points. Also, for b > 0, the given function is concave up with the given critical point.

(c)

To Conclude:

The inequality from earlier solution.