21: Derivative is

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

Since f is continuous at −1, the first two intervals can be connected; f is decreasing on (−∞,0]. Since f is continuous at 1, the last two intervals can be connected; f is increasing on [0,∞).

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

Remark: f ′(−1) = −∞ and f ′(1) = ∞; there is a vertical tangent line at these two points.

Now determine concavity using f ′′.

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