Science:Math Exam Resources/Courses/MATH110/April 2018/Question 07 (c)
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Question 07 (c) 

Let . (c) Find the intervals where is increasing and the intervals where it is decreasing. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

If on an interval , then is increasing on the interval. On the other hand, if on an interval , then is decreasing on the interval. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We first find the derivative of . Using the quotient rule, we get Since is always positive and is positive except for , the sign of the first derivative depends on . Indeed, if while if or . Therefore, the statement in the Hint implies that is increasing on and decreasing on . Note that is undefined at , because the denominator vanishes at this point. Answer: 