MATH110 April 2012
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Question 05 (f)
(f) Determine where ƒ is concave up and where it is concave down.
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We determine whether f is concave up or concave down by checking the sign of the second derivative, .
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From the previous question, we know that
Using the quotient rule, we calculate the second derivative
For this fraction, the numerator is always positive so we need only check the sign of the denominator. The denominator is zero when . For , the denominator is positive, for the denominator is negative, and then for the denominator is again positive. Thus we have that the function is concave up on and concave down on .
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