Answer Happy

- 216x, find the first derivative, g'(x). Given the function g(x) = 6x3 + 9x2 g'(x) = - Notice that g'(x) = 0 when x = - 4, that is, g'( – 4) = 0. = – 4, so we will use Now, we want to know whether there is a local minimum or local maximum at x = the second derivative test. Find the second derivative, g"(x). g"(x) = = Evaluate g"( – 4). 9"( – 4) = = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = - 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 x = – 4? [Answer either minimum or maximum -- watch your spelling!!] At x = 4 there is a local