Science:Math Exam Resources/Courses/MATH100/December 2015/Question 10 (g)
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Question 10 (g) 

Let . (g) Find the intervals on which is increasing. Find the intervals on which is decreasing. 
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If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

A function is increasing when and decreasing when . 
Hint 2 

In the expression of which part really determines its sign. 
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Solution  

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Please rate my easiness! It's quick and helps everyone guide their studies. We need to determine the sign of. From part (e) we have , where is always positive so it doesn't have any role in the sign. We only need to determine the sign of . From part (f) is at , so we make a sign chart for to find where it is positive and negative and therefore where the function is increasing and decreasing.
Intervals that is decreasing: . Intervals that is increasing: . 