Given the function g(x) = 8x-12x - 480x, find the first derivative, g'(x). g'(x) = 24x 24x - 480 Notice that g'(z) = 0 when x = 5, that is, g'(5) = 0. Now, we want to know whether there is a local minimum or local maximum at x = 5, so we will use the second derivative test. Find the second derivative, g"(x). g'(x) = Evaluate g"(5). g" (5) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = 5? [Answer either up or down At t BEK == watch your spelling!!] 5 the graph of g(x) is concave Based on the concavity of g(x) at x =5, does this mean that there is a local minimum or local maximum at x = 5? [Answer either minimum or maximum -- watch your spelling!!] At 2 - 5 there is a local