In this question, we will consider the function (a) Use asymptotics (as in the first week of class) to make a quick sketch of f(x). Use this sketch alone to decide which features the curve has. Select all that apply. f(x) has at least one root f(x) has at least one critical point f(x) has at least one global minimum ☐ f(x) has at least one global maximum f(x) has at least one local minimum ☐ f(x) has at least one local maximum f(x) has at least one inflection point (b) List the x-values of all roots of f(x). 0,9 (c) List the x-values of all critical points of f(x). 0, 27/4 B f(x)=x9x3. (d) Use interval notation to indicate where f(x) is increasing. (A function is increasing if larger -values give larger y-values. Don't include points where the function changes from increasing to decreasing, or from decreasing to increasing.) Increasing for a in: (27/4, Inf) (e) Use interval notation to indicate where f(x) is decreasing. (A function is decreasing if larger -values give smaller y-values. Don't include points where the function changes from increasing to decreasing, or from decreasing to increasing.) Decreasing for in: (f) List the x-values of all local maxima of f(x). x-values of local maxima = NONE (g) List the x-values of all local minima of f(x). -values of local minima = 27/4 B 目 (h) Use interval notation to indicate where f(x) is concave up. Concave up for a in: (-Inf,0)U(9/2,Inf) (i) Use interval notation to indicate where f(x) is concave down. Concave down for x in: (0,9/2) (j) List the x-values of all the inflection points of f. -values of inflection points = 0, 9/2 (k) Use all of the preceding information to sketch a graph of f. After you have made the sketch on your own, click "hint" to see what it should look like, and compare. (You cannot hand this in with WeBWorK, but it is an important skill to practice.) Hint: local/global min 6.75 W IP 4.5 IP