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Concept explainers
Using a graphing utility, graph for .
(a) Find the of the graph of .
(b) Approximate any
(c) Determine where is increasing and where it is decreasing.
(d) Without using a graphing utility, repeat parts (b)-(d) for .
(e) Without using a graphing utility, repeat parts (b)-(d) for .
(f) Without using a graphing utility, repeat parts (b)-(d) for .
![Check Mark](/static/check-mark.png)
To find:
a. Using a graphing utility, graph for .
Explanation of Solution
a. Using a graphing utility, graph for .
![Check Mark](/static/check-mark.png)
To find:
b. Find the of the graph of .
Explanation of Solution
b. Find the of the graph of .
To find put .
The are .
![Check Mark](/static/check-mark.png)
To find:
c. Approximate any local maxima and local minima.
Explanation of Solution
c. Approximate any local maxima and local minima.
From the graph,
The function has at .
at .
![Check Mark](/static/check-mark.png)
To find:
d. Determine where is increasing and where it is decreasing.
Explanation of Solution
d. Determine where is increasing and where it is decreasing.
From the graph,
The function , Increasing at and .
Decreasing at .
![Check Mark](/static/check-mark.png)
To find:
e. Without using a graphing utility, repeat parts (b)–(d) for .
Explanation of Solution
e. (i) Find the for for
To find put .
and
and
The are 2, 4, 6.
(ii) To find the local maxima and local minima:
Find the first derivative, for
We get,
Set the derivative equal to zero and solve for ,
Put in ,
We get,
Hence at
Put in ,
We get,
Hence at
(iii) The function is increasing at and
Decreasing at
![Check Mark](/static/check-mark.png)
To find:
f. Without using a graphing utility, repeat parts (b)–(d) for .
Explanation of Solution
f. (i) Find the for for
To find put
and
and
The are , 0, 1
(ii) To find the local maxima and local minima:
Find the first derivative, for
We get,
Set the derivative equal to zero and solve for ,
and
Put in
We get,
Hence at
Put in
We get,
Hence at
(iii) The function is increasing at and
Decreasing at
![Check Mark](/static/check-mark.png)
To find:
g. Without using a graphing utility, repeat parts (b)–(d) for .
Explanation of Solution
g. (i) Find the for for
To find put
and
and
The are , 0, 2
(ii) To find the local maxima and local minima:
Find the first derivative, for
We get,
Set the derivative equal to zero and solve for ,
and
Put in
We get,
Hence at
Put in
We get,
Hence at
(iii) The function is decreasing at and
Increasing at
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
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