MATH102 December 2013
• QA 1 • QA 2 • QA 3 • QA 4 • QA 5 • QA 6 • QA 7 • QA 8 • QB 1 • QB 2 • QB 3 • QB 4 • QB 5 • QB 6 • QB 7 • QB 8 • QC 1 • QC 2(a) • QC 2(b) • QC 2(c) • QC 2(d) • QC 3 • QC 4 •
Question A 01
Let . Which of the following conditions describes all values of a for which f HAS inflection points?
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How are inflection points related to the second derivative?
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has an inflection point wherever changes sign. Thus we begin by looking for the zeroes of :
Solving for a, we find that . Since , we have .
But by the same inequalities, when . Similarly, when . In these cases, has no inflection points since does not change sign.
Therefore . This is equivalent to answer .
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