Given the function $g(x) = 6x^3 - 63x^2 + 180x$, find the first derivative, $g'(x)$.\\
$g'(x) = 18x^2 - 126x + 180$\\
Notice that $g'(x) = 0$ when $x = 2$. That is, $g'(2) = 0$.\\
Now, we want to know whether there is a local minimum or local maximum at $x = 2$, so we will use the\\
second derivative test.\\
Find the second derivative, $g''(x)$.\\
$g''(x) = $\\
Evaluate $g''(2)$.\\
$g''(2) = $