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 ′′.
Next hint
Answer