Given the function g(x) = 8x3 + 24x2 - 72x, find the first derivative, g'(x). g'(x) = Notice that g' (x) = 0 when x = - 3, that is, g' ( -13) = 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'' (ac). g' ' (a ) = Evaluate g'' ( - 3). g"( - 3) = Based on the sign of this number, does this mean the graph of g(a) is concave up or concave down at x = - [Answer either up or down -- watch your spelling!] At x = - 3 the graph of g(x) is concave Based on the concavity of g(x) at a = - 3, does this mean that there is a local minimum or local maximum at x = - 3? [Answer either minimum or maximum -- watch your spelling!] At x = - 3 there is a local