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The local minimum of the function $f$ is at the point $x=1$, the function does not have a local maximum.

The local maximum of the function $f$ is at the point $x=0$, the local minimum at $x=1$.

The local maximum of the function $f$ is at the point $x=1$, the function does not have a local minimum.

The function $f$ has neither local minimum nor maximum.