Concept explainers
a.
Tofindthe interval on which the function
a.
Answer to Problem 4RE
The function is then increasing for
Explanation of Solution
Given information:
The given function is
Formula:
Chain rule:
Consider the function
Using product and chain rule:
Here
Now setting the derivative equal to zero to find the critical values,
Therefore, the critical values are
From the critical values the possible intervals are
Now to determine which of the intervals is increasing,
Consider
Consider
Consider
Therefore, the function is increasing for
b.
To find the interval on which the function
b.
Answer to Problem 4RE
The function is then decreasing for
Explanation of Solution
Given information:
The given function is
Formula:
Chain rule:
Consider the function
Using product and chain rule:
Here
Now setting the derivative equal to zero to find the critical values,
Therefore, the critical values are
From the critical values the possible intervals are
Now to determine which of the intervals is decreasing,
Consider
Consider
Consider
Therefore, the function is decreasing for
c.
To find the interval on which the function
c.
Answer to Problem 4RE
The function is concave up for
Explanation of Solution
Given information:
The given function is
Formula:
Chain rule:
Consider the function
Using product and chain rule:
Find second derivative,
The function is undefined whenever the denominator is equal to zero.
Therefore, the inflection points are at
Inflection point at
is not in the domain of the function.
Consider
Consider
Therefore, the function is concave up from
d.
To find the interval on which the function
d.
Answer to Problem 4RE
The function is concave down for
Explanation of Solution
Given information:
The given function is
Formula:
Chain rule:
Consider the function
Using product and chain rule:
Find second derivative,
The function is undefined whenever the denominator is equal to zero.
Therefore, the inflection points are at
Inflection point at
is not in the domain of the function.
Consider
Consider
Therefore, the function is concave down from
e.
To find the interval on which the function
e.
Answer to Problem 4RE
The function haslocal maximum values at
Explanation of Solution
Given information:
The given function is
Formula:
Chain rule:
Consider the function
Using product and chain rule:
Here
Now setting the derivative equal to zero to find the critical values,
The domain of
Consider
Consider
Consider
Since
Since
Therefore, the function has local maximum values at
f.
To find the interval on which the function
f.
Answer to Problem 4RE
The function hasinflection point at
Explanation of Solution
Given information:
The given function is
Formula:
Chain rule:
Consider the function
Using product and chain rule: 6
Find second derivative,
The sign of
When
When
When
Now to determine the sign of
Therefore, the function has inflection point at
Chapter 5 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus (10th Edition)
University Calculus: Early Transcendentals (4th Edition)
Calculus & Its Applications (14th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
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