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Y and A Tutoring Paper 2 with Answers and Hints · Q5

Paper 2CalculusAlgebra

Consider the following two statements about the polynomial p(x)p(x) with exactly two stationary points at x=ax=a and x=bx=b where a<ba<b.

P: p(x)p(x) has a maximum at x=ax=a

Q: p′(x)<0p'(x)<0 for a<x<ba<x<b

Which of the following is correct?

AP is necessary and sufficient for Q
BP is not necessary and not sufficient for Q
CP is necessary but not sufficient for Q
DP is sufficient but not necessary for Q

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