Science:Math Exam Resources/Courses/MATH100/December 2014/Question 08 (e)
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Question 08 (e) 

Let . Note is the natural logarithmic function, also denoted (e) Find the intervals where is increasing, and the intervals where is decreasing. Find the coordinates of local maximum and minimum if they exist. 
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 

Consider the derivative of and how it being positive or negative relates to being increasing or decreasing. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. First find the derivative
So the derivative exists everywhere on the domain. Any local maximum or minimum occur when . This is zero when , that is, when .
Hence gives the only local maximum at the coordinates and there is no local minimum. 