Science:Math Exam Resources/Courses/MATH 180/December 2017/Question 05 (b)
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Question 05 (b) 

Find all intervals where is concave down. 
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 function is concave down if it has negative second derivative. 
Hint 2 

We need to solve the inequality . 
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. By Hint 2, we need to solve the inequality . By the power rule, we have Therefore, we solve Since , the sign of the fraction is determined by the sign of the denominator. So this is the same as saying or Thus, the interval on which is concave down is .
Answer: The interval on which is concave down is . 