Show all supporting work for all problems. Let f (x) be the function defined by f (x) = In (2 + sin x) for n x 2m. 1. Find the critical numbers of f (x). 2. Determine the intervals of x where f(x) is increasing or decreasing. Justify your answers. 3. Find the absolute minimum value and the absolute maximum value of f (x) . Show the analysis that leads to your conclusion. 4. Find the x-coordinate of each inflection point on the graph of f (x) . Justify your answer. 5. Find the value(s) of x which satisfy the Mean Value Theorem for fon n Sx S 2x . Show the analysis that leads to your conclusion