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Clavis TMUA Set B Paper 2 · Q17

Paper 2Logic & proofCalculusFunctions & graphsAlgebra

The function ff is a polynomial with f(x)>0f(x)>0 for all real xx, and the function gg is defined for all real xx by

g(x)=∫0xf(t) dt.g(x)=\int_0^x f(t)\,dt.

Which of the following statements must be true?

  • I g(x)>0g(x)>0 for all real xx.
  • II gg is strictly increasing.
  • III g(−x)=−g(x)g(-x)=-g(x) for all real xx.
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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