MATH110 April 2011
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Question 08 (e)
Determine where ƒ is concave up and where it is concave down.
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A function's concavity is related to the sign of its second derivative.
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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.
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