Concept explainers
a.
Tofindthe interval on which the function
a.
Answer to Problem 7RE
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,
Consider
Consider
Therefore, the function is increasing for
b.
To find the interval on which the function
b.
Answer to Problem 7RE
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,
Consider
Consider
Therefore, the function is decreasing for
c.
To find the interval on which the function
c.
Answer to Problem 7RE
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,
Therefore, the function isconcave up for
d.
To find the interval on which the function
d.
Answer to Problem 7RE
The function is neverconcave down.
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,
Therefore, the function is never concave down.
e.
To find the interval on which the function
e.
Answer to Problem 7RE
The function haslocal minimum 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,
Hence at
Therefore, the function has local minimum at
f.
To find the interval on which the function
f.
Answer to Problem 7RE
The function has noinflection 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,
Here, the second derivative is negative for all values of
Hence, the function is defined for
Since
Therefore, the function has no inflection point.
Chapter 5 Solutions
Calculus: Graphical, Numerical, Algebraic
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