Science:Math Exam Resources/Courses/MATH110/April 2016/Question 05 (e)
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Question 05 (e)
(e) Find the intervals where is increasing and the intervals where it is decreasing.
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Calculate the derivative, and determine the intervals where and . When , is increasing, while , is decreasing.
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Let’s calculate the derivative first by the quotient rule,
Recall that the domain of in part (a) is . On the domain, the only solution of is .
Therefore, at the points , the derivative might change its sign. So, we make a partition of intervals in the real line based on these points and examine the sign of ;
(1) when , , so ;
(2) when , , so ;
(3) when , , so .
By the Hint, this tells us that is increasing in the interval , while it is decreasing in