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Official 2018 Paper 2 · Q6

Paper 2Logic & proof

Which one of the following functions provides a counterexample to the statement:

if f′(x)>0f'(x)>0 for all real xx, then f(x)>0f(x)>0 for all real xx.

Af(x)=x2+1f(x)=x^2+1
Bf(x)=x2−1f(x)=x^2-1
Cf(x)=x3+x+1f(x)=x^3+x+1
Df(x)=1−xf(x)=1-x
Ef(x)=2xf(x)=2^x

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