Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
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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
Book Icon
Chapter 3.1, Problem 80E

(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
Check Mark

Answer to Problem 80E

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

  Precalculus with Limits, Chapter 3.1, Problem 80E , additional homework tip 1

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

  Precalculus with Limits, Chapter 3.1, Problem 80E , additional homework tip 2

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

  Precalculus with Limits, Chapter 3.1, Problem 80E , 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
Check Mark

Answer to Problem 80E

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

  Precalculus with Limits, Chapter 3.1, Problem 80E , additional homework tip 4

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

  Precalculus with Limits, Chapter 3.1, Problem 80E , additional homework tip 5

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

  Precalculus with Limits, Chapter 3.1, Problem 80E , 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 .

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Chapter 3.1, Problem 79E
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Chapter 3.1, Problem 81E

Chapter 3 Solutions

Precalculus with Limits

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