Given the function g(x) = 6x + 45x2 + 72x, find the first derivative, g'(x). g'(x): Notice that g'(x) = O when a = -4, that is, g'(4) = 0. Now, we want to know whether there is a local minimum or local maximum at = 4, so we will use the second derivative test. Find the second derivative, g''(x). g'(x) = Evaluate g''(-4). g'(-4)= Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at = -4? [Answer either up or down - watch your spelling!!] At x = -4 the graph of g(x) is concave Based on the concavity of g(x) at x = -4, does this mean that there is a local minimum or local maximum at = [Answer either minimum or maximum -- watch your spelling!!] At = - 4 there is a local