Function that has a point with zero derivative and that point is not maximum nor minimum and not inflection point

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Can you find an example of a function that has a point with zero derivative and that point is not maximum nor minimum and not inflection point?

Thanks for the help.

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What about $f(x)=x^a\sin(1/x)$ with $a>0$ extended by continuity at $0$. Are you able to find $a$ such that the given conditions are satisfied?