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TMUAmockz Set 1 Paper 2 · Q10

Paper 2Logic & proofCalculus

Given that f′′(x)>0f''(x)>0 for all xx with 0≤x≤10\le x\le1, which of the following statements must be true?

  • I. f(12)<f(0)+f(1)2f\left(\dfrac12\right)<\dfrac{f(0)+f(1)}2
  • II. ∫01f(x)dx<f(12)\displaystyle\int_0^1f(x)\dd x<f\left(\dfrac12\right)
  • III. f′(0)<f(1)−f(0)f'(0)<f(1)-f(0)
AI only
BII only
CIII only
DI and II only
EI and III only
FI, II and III

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