6: Derivative is

Critical points:

f = 0 for x = −2; f ′ is suspect x = 5/2.

Can the two neighboring intervals of the same monotonicity be connected? Since f is continuous there, they can. f is increasing on [−2,∞).

There is no local maximum; local minimum f (−2) = −36.

Remark: One-sided derivatives at the connecting point are

They are not equal, so there is no derivative at x = 5/2.

Now determine concavity using f ′′.

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Answer