Math 1200, Calculus - Business and Social Sciences 4. You are given the following information about an unknown function g(x). . g(x) is defined on (-0o, co). . g'(x) is undefined when x = 3. . g(x) is positive on (-5, 1) U (7, 00). . g'(x) is positive on (-0o, 3) U (5, 00). . g(x) is negative on (1, 7). . g'(x) is negative on (3, 5). . g(x) is zero when x = 1 and when a = 7. . g'(x) is zero when x = 5. (a) (2 points) What is the domain of g(x)? (-00,00 ) (b) (5 points) When x = 2, is g(x) increasing or decreasing? Explain how you know. Increasing g ( xx ) = 70 c) (4 points) List the x values of any stationary points of g(x). Explain how you found them. If there are no stationary points, explain why there are none. d) (4 points) List the x values of any singular points of g(x). Explain how you found them. If there are no singular points, explain why there are none. (e) (6 points) List the a values of any local maxima of g(x). Explain how you know they are maxima. If g(x) has no maxima, explain how you know. 5