QuestionGiven the function $g(x)=6 x^{3}+18 x^{2}-144 x$, find the first derivative, $g^{\prime}(x)$. $$g^{\prime}(x)=$$ $\square$ Notice that $g^{\prime}(x)=0$ when $x=-4$, that is, $g^{\prime}(-4)=0$. Now, we want to know whether there is a local minimum or local maximum at $x=-4$, so we will use the second derivative test. Find the second derivative, $g^{\prime \prime}(x)$. $$g^{\prime \prime}(x)=$$ $\square$ Evaluate $g^{\prime \prime}(-4)$. $$g^{\prime \prime}(-4)=$$ $\square$ Based on the sign of this number, does this mean the graph of $g(x)$ is concave up or concave down at $x=-4$ ? At $x=-4$ the graph of $g(x)$ is Select an answer $v$ Based on the concavity of $g(x)$ at $x=-4$, does this mean that there is a local minimum or local maximum at $x=-4$ ? At $x=-4$ there is a local Select an answer $\checkmark$