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To determine the critical numbers of g(x), set g'(x) equal to zero and solve for...

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Basic Math

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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 linecan be divided into two intervals (-?, 1) and (1, ?). Determine the sign of g'(x) at one test value in each ofthe 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.

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