To Prove: The given inequality satisfying the given condition.

Question

Want to see the full answer?

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.

A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as: dx/dt = k(a-x)(b-x) where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?

Consider a body of mass m dropped from rest at t = 0. The body falls under the influence of gravity, and the air resistance FD opposing the motion is assumed to be proportional to the square of the velocity, so that FD = kV2. Call x the vertical distance and take the positive direction of the x-axis downward, with origin at the initial position of the body. Obtain relationships for the velocity and position of the body as a function of time t.

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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

Want to see the full answer?

Check out a sample textbook solution

See solution

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

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

Want to see the full answer?

Check out a sample textbook solution

See solution

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.

Want to see the full answer?

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.