Science:Math Exam Resources/Courses/MATH110/April 2011/Question 08 (e)
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Question 08 (e) 

Let Determine where ƒ is concave up and where it is concave down. 
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Hint 

A function's concavity is related to the sign of its second derivative. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We find the second derivative of by using the quotient rule on the first derivative: We find possible inflection points by setting equal to zero and also by determining where it is undefined. In this case, is never zero and is undefined when . Because these points are not included in our domain, ƒ has no inflection points, i.e. ƒ does not change its concavity. Therefore, it suffices to find the concavity at any point in the domain, e.g. at x = 0: and hence ƒ is concave down on its whole domain. 