Step 1 To determine the intervals on which the function is increasing or decreasing first find the critical numbers of the given

Question

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 Step 2 To determine the critical numbers of g x set g x equal to zero and solve for x g x 0 2 x 11 2x 2 0 g 0 g 0 20 g 0 0 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 1 and 1 Determine the sign of g x at one test value in each of the two intervals X First consider the interval 1 Let x 0 g x 2 x 1 1 2x2 0 1 1 1 Step 4 Since g 0 0 for which interval is the function decreasing Enter your answer using interval notation 0 1 00 1 Step 5 Now consider the interval 1 Let x 2 g x 2 x 1 g 2 2 g 2 2 1

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