Two Valleys, One Bottom

$x = 0$ is the global minimum: $f'(0) = 0$ and $f''(0) > 0$, so nothing can be lower.

$x = 1$ is a local minimum that is not the global minimum.

$f$ has local minima at $x = 0$ and $x = 3$; the global minimum is at $x = 3$, where $f = -27$.

$f$ has no global minimum, because $f(x) \to +\infty$ as $x \to \pm\infty$.