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Let the function $$f$$ be given by
$$f(x) =ย \begin{cases}-(x -1)^4; & x \leq 2\\(x - 3)^3; & x > 2\end{cases}$$
Then local extrema of $$f$$ exist at
$$x = 1$$ and $$x = 3$$
$$x = 1$$ and $$x = 2$$
$$x = 2$$ and $$x = 3$$
$$x = 1, x = 2$$ and $$x = 3$$
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