a.
To find: To find the increasing intervals for the function
a.
Answer to Problem 3RE
The function is increasing at
Explanation of Solution
Given information: The given function is
Formula used: Product rule:
Calculation:
The above equation is rewritten as,
Using the product rule finding the derivative for the above equation,
Simplifying to get,
Since
Therefore, the critical values are
The possible intervals for the critical values are
Now testing the above intervals to determine the increasing functions,
Take
Take
Take
Take
Therefore, the function is then increasing for
b.
To find: To find the decreasing intervals for the function
b.
Answer to Problem 3RE
The function is decreasing at
Explanation of Solution
Given information: The given function is
Calculation:
The given function is,
By using product and chain rule,
The factor
The value of
By entering any value from the observed period into the expression and noting the sign, the sign of over four intervals are
Therefore, the function is then decreasing for
c.
To find: To find the concave up for the function
c.
Answer to Problem 3RE
The function is concave up for
Explanation of Solution
Given information: The given function is
Calculation:
The above equation is rewritten as,
Using the product rule finding the derivative for the above equation,
Simplifying to get,
To find the second derivative,
To find the value of
As a result, there are no x values because this has no real solutions.
Substitute the value less than
The function
Therefore, the function is concave up for
d.
To find: To find the concave down for the function
d.
Answer to Problem 3RE
The function does not have concave down intervals.
Explanation of Solution
Given information: The given function is
Calculation:
The above equation is rewritten as,
Using the product rule finding the derivative for the above equation,
Simplifying to get,
To find the second derivative,
To find the value of
As a result, there are no x values because this has no real solutions.
Substitute the value less than
The function
Therefore, the function does not have intervals at concave down.
e.
To find: To find the local extreme values for the function
e.
Answer to Problem 3RE
The local extreme values have local minimums at
Explanation of Solution
Given information: The given function is
Calculation:
The above equation is rewritten as,
Using the product rule finding the derivative for the above equation,
Simplifying to get,
Since
Therefore, the critical values are
The possible intervals for the critical values are
Now testing the above intervals to determine the increasing functions,
Take
Take
Take
Take
For all the values of
The value of
So, there will be local minimum values.
To find the value of
Therefore, the local extreme values have local minimums at
f.
To find: To find the inflection points for the function
f.
Answer to Problem 3RE
The function does not have inflection points.
Explanation of Solution
Given information: The given function is
Calculation:
The above equation is rewritten as,
Using the product rule finding the derivative for the above equation,
Simplifying to get,
To find the second derivative,
To find the value of
As a result, there are no x values because this has no real solutions.
Substitute the value less than
Since
Therefore, the function does not have any point of inflection.
Chapter 4 Solutions
CALCULUS-W/XL ACCESS
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