please solve these problems. there are five problems. please show me all of your work.

1.

Consider the function f(I) = et sinx on the closed interval 0, 3]. . (2 points) Compute f'(I). . (2 points) Determine which critical points of f lie in (0, 3). . (2 points) Determine the absolute minimum and marimum value that f attains on [0, 3].Determine the location and value of the absolute extreme values of fon the given interval, if they exist. f(x) = 5 cos 2x on [0, it] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice (Type an exact answer, using it as needed. Use a comma to separate answers as needed.) O A. The absolute minimum is at x = but there is no absolute maximum O B. The absolute maximum is at x= but there is no absolute minimum O C. The absolute maximum is at x = and the absolute minimum is at x = O D. There are no absolute extreme values for f(x) on [0, It]Find the critical points of the following function. f(x) = In x X Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical point(s) occur(s) at x = (Use a comma to separate answers as needed.) O B. There are no critical points.Determine whether Rolle's theorem applies to the function shown below on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle's theorem. f(x) = 5- x4/ 8; [- 1,1] Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. Rolle's Theorem applies and the point(s) guaranteed to exist is/are x = (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) O B. Rolle's Theorem does not applyDetermine whether Rolle's theorem applies to the function shown below on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle's theorem. f(x) = - cos 2x, 4 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. Rolle's Theorem applies and the point(s) guaranteed to exist is/are x = (Type an exact answer, using it as needed. Use a comma to separate answers as needed.) O B. Rolle's Theorem does not apply