213 The function graphed above is: Increasing on the interval(s) Decreasing on the interval(s) Given the function g(x) = 8x3 + 24x2 - 192x. Find the first derivative, g'(x). g'(x) = Notice that g'(x) = 0 when I = - 4, that is, g'( - 4) = 0. We will use the second derivative test to determine whether there is a local minimum or local maximum at I = - 4. Find the second derivative, g"(I). g"(I) = Evaluate g" '( - 4). g"(-4) = Based on the sign of g"'( - 4) at : = - 4, the graph of g(x) is O Concave Up O Concave Down Based on the concavity of g(x) at = = - 4, at I = - 4 there is a local O Minimum O Maximum