QPaperGen

\[
g(x) = x^3 - 3x \Rightarrow g'(x) = 3x^2 - 3 = 3(x^2 - 1) = 3(x - 1)(x + 1)
\]
Setting \( g'(x) = 0 \Rightarrow x = \pm 1 \)

\[
g''(x) = 6x
\Rightarrow g''(1) = 6 > 0 \Rightarrow \text{Local minimum at } x = 1
\]
\[
g(1) = 1 - 3 = -2
\]
\[
g''(-1) = -6 < 0 \Rightarrow \text{Local maximum at } x = -1
\]
\[
g(-1) = -1 + 3 = 2
\]