Given the function g(x) - 6x3 - 27x2 + 36x, find the first derivative, g' (x). g' (a ) = Notice that g'(a) = 0 when a = 2, that is, g' (2) = 0. Now, we want to know whether there is a local minimum or local maximum at x = 2, so we will use the second derivative test. Find the second derivative, g''(a). g' '(a ) = Evaluate g' ' (2). g''(2) = Based on the sign of this number, does this mean the graph of g(a) is concave up or concave down at x = 2? [Answer either up or down -- watch your spelling!] At x = 2 the graph of g(a) is concave Based on the concavity of g(a ) at a = 2, does this mean that there is a local minimum or local maximum at x = 2? [Answer either minimum or maximum -- watch your spelling!] At x = 2 there is a local