30: Derivative is

Critical points:

f ′ is suspect at x = 1 and x = 4.

Local maximum f (3) = 1; local minimum f (1) = −3 and f (4) = 0.

Remark: One-sided derivatives at the connecting points are

They are not equal, so there is no derivative at x = 1.

They are not equal, so there is no derivative at x = 4.

Now determine concavity using f ′′.

Next hint
Answer