(a)
To find: The interval on which given function is increasing.
(a)
Answer to Problem 11RE
The given function increases in the interval
Explanation of Solution
Given:
The function is
Calculation:
The derivative of the function is:
When
Hence,
Intervals | ||
Sign of y’ | - | + |
Nature | Decreasing | Increasing |
Conclusion:
The given function increases in the interval
(b)
To find: The interval on which given function is decreasing.
(b)
Answer to Problem 11RE
The given function increases in the interval
Explanation of Solution
Given:
The function is
Calculation:
Intervals | ||
Sign of y’ | - | + |
Nature | Decreasing | Increasing |
Conclusion:
The given function increases in the interval
(c)
The interval in which function is concave up.
(c)
Answer to Problem 11RE
The function is not concave up in any interval.
Explanation of Solution
Given:
The function is
Calculation:
The second derivative of the function is:
As, the second derivative is negative therefore, the function is not concave up. It is concave down.
Conclusion:
The function is not concave up in any interval.
(d)
The interval in which function is concave down.
(d)
Answer to Problem 11RE
The function is concave down in
Explanation of Solution
Given:
The function is
Calculation:
The second derivative of the function is:
The function is concave down because the second derivative is negative.
The interval is between
Conclusion:
The function is concave down in
(e)
The local extreme values.
(e)
Answer to Problem 11RE
The local extreme and absolute
Explanation of Solution
Given:
The function is
Calculation:
The interval is between
Conclusion:
The local extreme and absolute maxima is at
(f)
The inflection points.
(f)
Answer to Problem 11RE
There are no inflection points.
Explanation of Solution
Given:
The function is
Calculation:
The function is concave down so, there is no inflection point.
Conclusion:
There are no inflection points.
Chapter 4 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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