Science:Math Exam Resources/Courses/MATH100/December 2015/Question 10 (h)
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Question 10 (h) 

Let . (h) The second derivative is . Find the xcoordinates of any points of inflection. You must explain your answer. 
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 

Inflection points of a function are the points at which and changes sign in their neighborhood. 
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Solution  

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Please rate my easiness! It's quick and helps everyone guide their studies. First, we should find the points where .
Again the last equation never happens, so .
We check the sign of for 's such that , for example which results in the following sign chart:
Intervals that is concave down: . Inflection points: . 