Science:Math Exam Resources/Courses/MATH 180/December 2017/Question 04 (c)
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Question 04 (c) 

Find all values where the graph of has a horizontal tangent line. 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

A horizontal line has zero slope (derivative). 
Hint 2 

The question is equivalent to solving . 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. Using quotient rule with , , and , we have By Hint 2, we need to find those that satisfies . By the above factorization of , we see that if and only if or , that means or . (Note that the denominator of is not vanished at and , so that is defined at those points.) In other words, the values at which has a horizontal tangent line are and .
Answer: 