with detailed solution clear handwritten

1. Verify that the Mean Value Theorem applies to {2 points) h(?) : ln(;r2 43: + 4] on the interval [53, e + 2]. and write the conclusion of the theorem. 2. Let f be a function that is continuous everywhere except at m : 2, such that f(0) = 0 and f(3) = f(3) = 4. Moreover, suppose that f(3) : 4, lim f(it') : oo, lim f(33) : +00, and ,lil_lf(3:) I] : 0. The table of :r:}2 IPQ'l' signs for f' and f\" is given below. a. Give the equations of all the asymptotes of the graph of f. {I point) b. Determine the intervals where f is increasing or decreasing, and where f is concave up or concave down. Give the coordinates of the relative extremurn point(s)and of the point(s) of inection of the graph of f. {3.5 points) c. Sketch the graph of f with emphasis on concavity. Draw the asymptotes and label all the intercept point(s)1 relative extremum point(s), and point(s) of inflection with their respective coordinates. {3.5 points)