a.
To find: To find the increasing intervals for the function
a.
![Check Mark](/static/check-mark.png)
Answer to Problem 4RE
The function is increasing at
Explanation of Solution
Given information: The given function is
Formula used: Product rule:
Calculation:
The above equation is,
Differentiating the function to get,
When
When
Therefore, the function increases at
b.
To find: To find the decreasing intervals for the function
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 4RE
The function is decreasing at
Explanation of Solution
Given information: The given function is
Formula used: Product rule:
Calculation:
The above equation is,
Differentiating the function to get,
When
When
Therefore, the function decreases at
c.
To find: To find the concave up for the function
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 4RE
The interval on which the function is concave up is
Explanation of Solution
Given information: The given function is
Formula used: Product rule:
Calculation:
The above equation is,
Differentiating the function to get,
Using quotient and chain rule, find
The value of
So, the value of
For
For
Therefore, the interval on which the function is concave up is
d.
To find: To find the concave down for the function
d.
![Check Mark](/static/check-mark.png)
Answer to Problem 4RE
The interval on which the function is concave down is
Explanation of Solution
Given information: The given function is
Calculation:
The above equation is,
Differentiating the function to get,
Using quotient and chain rule, find
The value of
So, the value of
For
For
Therefore, the interval on which the function is concave down is
e.
To find: To find the local extreme values for the function
e.
![Check Mark](/static/check-mark.png)
Answer to Problem 4RE
The local extreme values have local minimums at
Explanation of Solution
Given information: The given function is
Calculation:
The above equation is,
Differentiating the function to get,
When
When
The domain value is
The intervals of the functions are
For
For
For
For
For
To determine the
Therefore, the local extreme values have local minimums at
f.
To find: To find the inflection points for the function
f.
![Check Mark](/static/check-mark.png)
Answer to Problem 4RE
The function has the inflection point at
Explanation of Solution
Given information: The given function is
Calculation:
The above equation is,
Differentiating the function to get,
Using quotient and chain rule, find
The value of
So, the value of
For
For
Since
Therefore, the function has the inflection point at
Chapter 4 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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