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 ′′.
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