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High School Math Calculus CALCULUS-W/XL ACCESS

The value of local maximum .

The value of local maximum .

CALCULUS-W/XL ACCESS

CALCULUS-W/XL ACCESS

6th Edition

ISBN: 9781418300197

Author: Finney

Publisher: PEARSON

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Question

Chapter 4, Problem 17RE

(a)

To determine

To find: The value of local maximum.

(a)

Expert Solution

Answer to Problem 17RE

The answer: no local maximum

Explanation of Solution

Given information:

The function is y′=6(x+1)(x−2)2

Calculation:

Where, y′=0

So,

y ′ =6(x+1) (x−2) 2 =6 x 3 −3 x 2 +4 0=6(x+1) (x−2) 2 x=−1,2

And

y″=63x2−6x=18x(x−2)y″(−1)=54>0 concave up x=−1 is a local minimum

Then,

y″(2)=0

Intermediate

y′(0)=24>0

Increasing

y′(3)=24>0

Increasing.

Therefore, the required no local maximum of the given function.

(b)

To determine

To find: The value of local minimum.

(b)

Expert Solution

Answer to Problem 17RE

The answer: local minimum at x=−1

Explanation of Solution

Given information:

The function is y′=6(x+1)(x−2)2

Calculation:

Where, y′=0

So,

y ′ =6(x+1) (x−2) 2 =6 x 3 −3 x 2 +4 0=6(x+1) (x−2) 2 x=−1,2

And

y″=63x2−6x=18x(x−2)y″(−1)=54>0 concave up x=−1 is a local minimum

Then,

y″(2)=0

Intermediate

y′(0)=24>0

Increasing

y′(3)=24>0

Increasing.

Therefore, the required local minimum at x=−1 .

(c)

To determine

To find: The value of inflection point.

(c)

Expert Solution

Answer to Problem 17RE

The answer: at x1=0 and

At x2=2 .

Explanation of Solution

Given information:

The function is y′=6(x+1)(x−2)2

Calculation:

f′(x)=6(x+1)x2−4x+4=6x3−4x2+4x+x2−4x+4=6x3−3x2+4f″(x)=6x3−3x2+4′=63x2−6x=18x(x−2)

Given that linear functions change their sign at their zeros, each of these numbers represent the values at which an inflection takes place.

Therefore, the required inflection points are at x1=0 and

At x2=2 .

Chapter 4, Problem 16RE

Chapter 4, Problem 18RE

Chapter 4 Solutions

CALCULUS-W/XL ACCESS

Ch. 4.1 - Prob. 1QR Ch. 4.1 - Prob. 2QR Ch. 4.1 - Prob. 3QR Ch. 4.1 - Prob. 4QR Ch. 4.1 - Prob. 5QR Ch. 4.1 - Prob. 6QR Ch. 4.1 - Prob. 7QR Ch. 4.1 - Prob. 8QR Ch. 4.1 - Prob. 9QR Ch. 4.1 - Prob. 10QR

Ch. 4.1 - Prob. 11QR Ch. 4.1 - Prob. 12QR Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - Prob. 48E Ch. 4.1 - 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