QuestionGiven the function $g(x)=8 x^{3}+24 x^{2}-360 x$ , find the first derivative, $g^{\prime}(x)$. $$g^{\prime}(x)=$$ $\square$ Notice that $g^{\prime}(x)=0$ when $x=3$, that is, $g^{\prime}(3)=0$ 。
Now, we want to know whether there is a local minimum or local maximum at $x=3$, so we will use the second derivative test.
Find the second derivative, $g^{\prime \prime}(x)$. $$g^{\prime \prime}(x)=$$ $\square$ Evaluate $g^{\prime \prime}(3)$. $$g^{\prime \prime}(3)=$$ $\square$ Based on the sign of this number, does this mean the graph of $g(x)$ is concave up or concave down at $x=3$ ? concave down concave up
Based on the concavity of $g(x)$ at $x=3$, does this mean that there is a local minimum or local