Science:Math Exam Resources/Courses/MATH104/December 2011/Question 02 (b)
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Question 02 (b) 

Consider the function Its first and second derivatives are given by and Find all such that or does not exist. 
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 

Try setting the numerator and the denominator to 0. What does a value of 0 in the numerator correspond to? How about when the denominator is 0? 
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. To determine where f"(x)=0, we look at the numerator of f"(x) and note that f"(x)=0 when the numerator is zero, i.e. Since x^{2}+9=0 has no real solutions, the only value of x that satisfies the above equation is when x=0.
So, f"(x) does not exist when .
