DETAILS PREVIOUS ANSWERS LARAPCALC10 3.2.028.SBS. MY NOTES ASK YOUR TEACHER PRA Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (If an answer does not exist, enter DNE.) \(g(x) = 12\left(1 + \frac{1}{x} + \frac{1}{x^2}\right), \quad [-5, 4]\) Step 1: Begin by finding the derivative of \(g(x)\). \(g'(x) =\) Step 2: Find the critical numbers and points of discontinuity. (Enter your answers as a comma-separated list.) \(x =\) Step 3: Test the interval. (If an answer is undefined, enter UNDEFINED.) x-value Endpoint \(x = -5\) Critical \(x = -2\) Discontinuity \(x = 0\) Endpoint \(x = 4\) \(g(x)\) Conclusion ---Select--- ---Select--- ---Select--- ---Select--- Step 4: Find the absolute extrema. (If an answer does not exist, enter DNE.) absolute maximum \((x, y) = \left(4, \frac{63}{4}\right)\) absolute minimum \((x, y) = (-2, 9)\)
