Given the function g(x) = 8x³ + 108x² + 480€, find the first derivative, gʻ(z). g'(x) = Notice that g'(x) = 0 when = 4, that is, g'( − 4) = 0. Now, we want to know whether there is a local minimum or local maximum at + = - 4, so we will use the second derivative test. Find the second derivative, g''(¹). g''(x) = Evaluate g''(-4). g''( − 4) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at I= -4? At z = - 4 the graph of g(x) is Select an answer Based on the concavity of g(x) at x = − 4, does this mean that there is a local minimum or local maximum at = - 4? At z = 4 there is a local Select an answer ✓ -