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Official 2019 Paper 2 · Q14

Paper 2Logic & proofAlgebra

Consider the following statements about the polynomial p(x)p(x), where a<ba<b:

  • I p(a)≤p(b)p(a)\leq p(b)
  • II p′(a)≤p′(b)p'(a)\leq p'(b)
  • III p′′(a)≤p′′(b)p''(a)\leq p''(b)

Which of these statements is a necessary condition for p(x)p(x) to be increasing for a≤x≤ba\leq x\leq b?

Anone of them
BI only
CII only
DIII only
EI and II only
FI and III only
GII and III only
HI, II and III

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