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Qiuyun TMUA Simulation Test Paper 2 · Q3

Paper 2Logic & proof

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

f′(x)>0f'(x)>0 is necessary for f(x)f(x) being strictly monotonic.

Af(x)=ln⁡x, x∈[0,+∞]f(x)=\ln x,\ x\in[0,+\infty]
Bf(x)=x5, x∈Rf(x)=x^5,\ x\in\R
Cf(x)=ex, x∈Rf(x)=e^x,\ x\in\R
Df(x)=x2, x∈Rf(x)=x^2,\ x\in\R
Ef(x)=x, x∈Rf(x)=x,\ x\in\R

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