Science:Math Exam Resources/Courses/MATH110/April 2016/Question 05 (e)
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Question 05 (e) 

Let (e) Find the intervals where is increasing and the intervals where it is decreasing. 
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Hint 

Calculate the derivative, and determine the intervals where and . When , is increasing, while , is decreasing. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. 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 