== Given the function g(x) = 8x-24x2-72x, find the first derivative, g'(x). g'(x) = Notice that g'(x) = 0 when x = 3, that is, g'(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'(x). g'(x) = Evaluate g"(3). g'(3) Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = 3? At x=3 the graph of g(x) is Select an answer == Based on the concavity of g(x) at x = 3, does this mean that there is a local minimum or local maximum at x = 3?