Science:Math Exam Resources/Courses/MATH102/December 2017/Question 11 (a)
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Question 11 (a) 

Consider the function
You are told that there is a critical point somewhere near the point .
(a) Is the critical point a local maximum, local minimum, or neither? 
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 

Recall the second derivative test: a critical point is a local minimum (respectively maximum) if the second derivative at the point is positive (respectively negative). 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let us first compute the derivatives: If is near , then is close to Therefore, by the second derivative test, the critical is a local minimum.
Answer: The critical point is a . 