4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

Concept explainers

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Maxima and Minima

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Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

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Question

Chapter 3.1, Problem 74E

(a)

To determine

To sketch: the graph of the functions, to find where the function is increasing and decreasing and approximate any relative maximum or minimum values.

(a)

Expert Solution

Answer to Problem 74E

The function is decreasing implies decreasing interval is (−∞,0)(2,∞) .

Explanation of Solution

Given information:

Given function

f(x)=x2e−x

Calculation:

Consider the function f(x)=x2e−x

Use the T1-83 calculator.

Enter the expression in the T1-83 calculator after pressing Y= button as shown below

EBK PRECALCULUS W/LIMITS, Chapter 3.1, Problem 74E , additional homework tip 1

Press the window button and adjust the window as shown below:

EBK PRECALCULUS W/LIMITS, Chapter 3.1, Problem 74E , additional homework tip 2

Click on the graph button and below is the graph of the expression

EBK PRECALCULUS W/LIMITS, Chapter 3.1, Problem 74E , additional homework tip 3

Use the TRACE button and then the arrow keys to move around the function curve. Observe the graph and find that the function is increasing between 0 and 2. Hence increasing interval is (0,2) . For remaining interval the function is decreasing implies decreasing interval is (−∞,0)(2,∞) .

Now with the help of TRACE option the peak and valley of the curve is found to be at 2 and 0 respectively. Hence the relative maximum occurs at x=2 and the relative minimum is at x=0

(b)

To determine

To sketch: the graph of the functions, to find where the function is increasing and decreasing and approximate any relative maximum or minimum values.

(b)

Expert Solution

Answer to Problem 74E

Decreasing interval is (1.44,∞) . For remaining interval the function is increasing implies increasing interval is (−∞,1.44) .

Explanation of Solution

Given information:

Given function

g(x)=x23−x

Calculation:

Consider the function g(x)=x23−x

Use the T1-83 calculator.

Enter the expression in the T1-83 calculator after pressing Y= as shown below

EBK PRECALCULUS W/LIMITS, Chapter 3.1, Problem 74E , additional homework tip 4

Press the WINDOW button and adjust the window as shown below:

EBK PRECALCULUS W/LIMITS, Chapter 3.1, Problem 74E , additional homework tip 5

Click on the graph button and below is the graph of the expression

EBK PRECALCULUS W/LIMITS, Chapter 3.1, Problem 74E , additional homework tip 6

Use the TRACE button and then the arrow keys to move around the function curve. Observe the graph and find the function is decreasing between 1.44 and infinite. Hence decreasing interval is (1.44,∞) . For remaining interval the function is increasing implies increasing interval is (−∞,1.44) . Now with the help of TRACE option the peak of the curve is found to be at 1.44.

Hence the relative maximum occurs at x=1.44 .

Chapter 3.1, Problem 73E

Chapter 3.1, Problem 75E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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