15: Derivative is

Critical points: f = 0 not possible; f ′ is suspect at x = 1 (note that 2x² − 2x + 1 is always positive).

There is no local maximum; local minimum f (1) = 0.

Remark: One-sided derivatives at the connecting point are

They are not equal, so there is no derivative at x = 1.

Now determine concavity using f ′′.

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Answer