Find the maximum and minimum values of the function given by $g(x) = x^{3} + 1$.

(NONE) The given function is $g(x) = x^{3} + 1$.
To find the critical points,we find the first derivative: $g'(x) = 3x^{2}$.
Setting $g'(x) = 0$,we get $3x^{2} = 0$,which implies $x = 0$.
For $x < 0$,$g'(x) > 0$ and for $x > 0$,$g'(x) > 0$.
Since the sign of $g'(x)$ does not change as $x$ passes through $0$,$x = 0$ is a point of inflection.
As $x \to \infty$,$g(x) \to \infty$ and as $x \to -\infty$,$g(x) \to -\infty$.
Therefore,the function $g(x) = x^{3} + 1$ has neither a local maximum nor a local minimum value.