Science:Math Exam Resources/Courses/MATH110/April 2011/Question 08 (d)
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Question 08 (d) |
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Let Determine where ƒ is increasing and 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 |
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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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Found a typo? Is this solution unclear? Let us know here.
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 . |