Find a strictly increasing function $ f$ with $ f'(1)=0$

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Find a strictly increasing function $ f$ with $ f'(1)=0$.

I've found the function $f(x)=\frac{x^3}{3}−x^2+x$

But I don't know how to prove that the function is strictly increasing.

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What about $f:\mathbb{R}\to\mathbb{R}$ defined by $f(x)=(x-1)^3$?