Answer
(a) $x = 0$ is the only critical point.
(b) $f$ has a local minimum of $f(0) = 3$ at $x = 0$.
(c) The absolute maximum is $12$ and the absolute minimum is $3$.
Work Step by Step
(a). $f'(x) = 2x$, so $x = 0$ is the only critical point.
(b). Note that $f' < 0$ for $x < 0$ and $f' > 0$ for $x > 0$, so $f$ has a local minimum of $f(0) = 3$ at $x = 0$.
(c). Note that $f(−3) = 12$, $f(0) = 3$ and $f(2) = 7$, so the absolute maximum is $12$ and the absolute minimum is $3$.
