Given the function $g(x)=4x^3+48x^2+180x,$ find the first derivative, $g^{\text{'}}(x).$

$g^{\text{'}}(x)=$

Notice that $g^{\text{'}}(x)=0$ when $x=-3,$ that $is,g^{\text{'}}(-3)=0.$

Now, $we$ want $to$ know whether there $is$ a local minimum $or$ local maximum $atx=-3,so$

$we$ will use the second derivative test.

Find the second derivative, $g^{\text{'}\text{'}}(x).$

$g^{\text{'}\text{'}}(x)=$