13: Derivative is

Critical points:

f ′ does not exist at x = 1 since f is not continuous there.

Can the two neighboring intervals of the same monotonicity be connected? f is not continuous so it is not automatic, a closer look is needed. f first grows to f (1^-) = f (1) = e, then it jumps up to f (1⁺) = 11 > e and continues as increasing. Thus connecting is possible and f is increasing on [0,3].

Local maxima f (−2) = 4/e² and f (3) = 27; local minimum f (0) = 0.

Remark: One-sided derivatives at the connecting point are

Now determine concavity using f ′′.

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Answer