8: Derivative is

Critical points: f = 0 for x = −1; f ′ does not exist at x = 0.

Local maximum f (−1) = 3; local minimum f (0) = 0.

Remark: One-sided derivatives at the connecting point are

They are not equal, so there is really no derivative at x = 0.

Now determine concavity using f ′′.

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Answer