Single Variable Calculus: Concepts and Contexts, Enhanced Edition

4th Edition

ISBN: 9781337687805

Author: James Stewart

Publisher: Cengage Learning

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Question

Chapter 4.3, Problem 28E

(a)

To determine

To find:The intervals of increase or decrease.

(a)

Expert Solution

Explanation of Solution

Given: $B(x)=3x2/3−x$

Calculate the first derivative of the given function.

$B′(x)=3⋅23x−1/3−10=2−x1/3x1/3x=0, 8$

The function is decreasing in the interval $(−∞, 0)$ .

The function is increasing in the interval $(0, 8)$

The function is decreasing in the interval $(8, ∞)$ .

(b)

To determine

To find :The local maxima and local minima.

(b)

Expert Solution

Explanation of Solution

The function is decreasing in the interval $(−∞, 0)$ .

The function is increasing in the interval $(0, 8)$

The function is decreasing in the interval $(8, ∞)$

The value of $B′$ is changing from negative to positive at $x=0$

So, the local minima is $(0, 0)$

The value of $B′$ is changing from positive to negative at $x=8$

So, the local maxima is $(8, 4)$

(c)

To determine

To find :The concavity of the function and the point of inflection.

(c)

Expert Solution

Explanation of Solution

Calculate the second derivative of the given function.

$B″(x)=−23x−4/3$

$B″(x)<0$ for the interval $−∞<x<0$ . So, the graph is concave down for $(−∞, 0)$

$B″(x)<0$ for the interval $0<x<∞$ . So, the graph is concave down for $(0, ∞)$

There is no change of sign so no inflection point.

(d)

To determine

To sketch :The graph of result obtained from part (a) to (c).

(d)

Expert Solution

Explanation of Solution

Given: $B(x)=3x2/3−x$

The graph of the result obtained is shown in figure below.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4.3, Problem 28E

Figure (1)

Therefore, the required graph is shown in figure (1).

Chapter 4.3, Problem 27E

Chapter 4.3, Problem 29E

Chapter 4 Solutions

Single Variable Calculus: Concepts and Contexts, Enhanced Edition

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

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