Science:Math Exam Resources/Courses/MATH100/December 2018/Question 05 (c)
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Question 05 (c) 

Let (c) Find the intervals on which is concave up and the intervals on which is concave down. 
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Hint 

If the function is concave up, the second derivative of the function is positive. For concave down, it is negative. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We have This denominator will always be nonnegative (because of the even number in the exponent), so it suffices to understand when the numerator is positive/negative. Note also that is undefined at . The numerator is zero when , positive when , and negative when . We therefore conclude that . 