To determine the critical numbers of g(x), set g'(x) equal

Last updated: 7/17/2022

To determine the critical numbers of g(x), set g'(x) equal to zero and solve for x. Since there is no point for which g'(x) does not exist, x = 1 is the only critical number. Thus, the number line can be divided into two intervals (-∞, 1) and (1, ∞). Determine the sign of g'(x) at one test value in each of the two intervals. First consider the interval (-∞, 1). Let x = 0. Since g'(0) < 0, for which interval is the function decreasing. (Enter your answer using interval notation.) Now consider the interval (1, ∞). Let x = 2. Since g'(2) > 0, for which interval is the function increasing.