24: Derivative is

Critical points: f = 0 for x = −1 and x = 1; f ′ is suspect at x = 0.

Since f is continuous at 0, the middle two intervals can be connected and f is increasing on [−1,1].

Local maximum f (−1) = 1/e; local minimum f (−1) = −1/e.

Remark: One-sided derivatives at the connecting point are

They are equal, so there is derivative at 0, namely f ′(x) = 1.

Now determine concavity using f ′′.

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