Step 1 To determine the intervals on which the function is increasing or decreasing, first find the critical numbers of the given function. Determine g'(x). g(x) = x-2x-360 g'(x) = 2x-2 2x-2 Step 2 To determine the critical numbers of g(x), set g'(x) equal to zero and solve for x. g'(x) = 0 2x-2=0 2(x - 1 = 0 x = 1 Step 3 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 (-co, 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. g'(x)=2(x1) g'(0) = 200 g'(0) = 2-1 -1 g'(0) -2 Step 4 Since g'(0) < 0, for which interval is the function decreasing. (Enter your answer using interval notation.) (-00,1) (-0,1) Step 5 Now consider the interval (1, ). Let x = 2. g'(x)=2(x 1) g'(2) = 2( g'(2) = 2( - 1)