Science:Math Exam Resources/Courses/MATH110/April 2011/Question 08 (d)
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Question 08 (d) 

Let Determine where ƒ is increasing and where it is decreasing. 
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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 

We determine where is increasing or decreasing by looking at the sign (positive or negative) of the first derivative. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. To determine where is increasing or decreasing, we look at the sign of the first derivative. The first derivative, calculated using the chain rule, is: It has critical points at . The values 2 and 2 are not part of the domain, but x = 0 is. We first note that the denominator is always negative on the domain . Hence, the sign of the derivative is always the opposite sign of the numerator. For x < 0 we see that , while for x > 0 we see that . Hence, is increasing on (2,0) and decreasing on (0,2).
Note. This also means that has a local maximum at . 