Science:Math Exam Resources/Courses/MATH100/December 2013/Question 08 (a)
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Question 08 (a) 

FullSolution Problem. Justify your answer and show your work. Full simplification of numerical answers is required unless explicitly stated otherwise. Let . Find the critical numbers of . 
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 

is said to be a critical number/point of if the slope of the tangent line to at is 0, or if the slope does not exist. 
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. By the definition of a critical number, we must find the for which or for which does not exist:
Therefore the critical numbers of are . 