Concept explainers
a.
Tofindthe interval on which the function
a.
Answer to Problem 8RE
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:
Set the derivative equal to zero,
Here we consider only the real value
Consider
Therefore, numerator is always positive for
Therefore, the function is increasing for
b.
To find the interval on which the function
b.
Answer to Problem 8RE
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:
Set the derivative equal to zero,
Here we consider only the real value
Consider
Consider
Consider
Therefore, the function is decreasing for
c.
To find the interval on which the function
c.
Answer to Problem 8RE
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:
Set the second derivative equal to zero,
Consider
Consider
Consider
Consider
Therefore, the function isconcave up for
d.
To find the interval on which the function
d.
Answer to Problem 8RE
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:
Set the second derivative equal to zero,
Consider
Consider
Consider
Consider
Therefore, the function is concave down for
e.
To find the interval on which the function
e.
Answer to Problem 8RE
The function haslocal maximum at
Explanation of Solution
Given information:
The given function is
Formula:
Chain rule:
Consider the function
Using product and chain rule:
Set the derivative equal to zero,
The two critical values are
Consider
Consider
Consider
Therefore, the function has local maximum at
f.
To find the interval on which the function
f.
Answer to Problem 8RE
The function hasinflection point
Explanation of Solution
Given information:
The given function is
Formula:
Chain rule:
Consider the function
Using product and chain rule:
Set the second derivative equal to zero,
Direction of concavity changes only around
Consider
Consider
Consider
Therefore, the function hasinflection point
Chapter 5 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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