Given the function g(x) = 4x + 18x2 - 120x, find the first derivative, g'(x). g'(x) = Notice that g'(x) = 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? At x = -5 the graph of g(x) is O concave down concave up Based on the concavity of g(x) at x=-5, does this mean that there is a local minimum or local maximum at x= At x= = - 5? - 5 there is a local O minimum maximum