1) A rectangular poster is to contain 338 square inches of print. The margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. What should the dimensions of the poster be (in inches) so that the least amount of poster is used? (Enter your answers as a comma-separated list.)

2) Find two positive numbers that satisfy the given requirements. (Enter your answers as a comma-separated list.)The sum is S and the product is a maximum.

3) At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 8 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate (in ft/min) is the height of the pile changing when the pile is 12 feet high? (Hint: The formula for the volume of a cone is V= 1/3pi r^2h)

Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your answers to four decimal places.) f(x) = tan(x), x1 = 0.3 Consider the following function and closed interval. f(x) = (x - 1)(x - 7)(x - 9), [1, 9] Is f continuous on the closed interval [1, 9]? Yes O No If f is differentiable on the open interval (1, 9), find f'(x). (If it is not differentiable on the open interval, enter DNE.) f' ( x ) = Find f(1) and f(9). f(1) = f(9) = Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). O No, because f(a) * f(b). If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.) C=The graph of for) is shown (see figure). 7x r = "0 m Ma r tam: n rob (a) Find the following limits. it: lim f(x) xsoo 3? || 5 A 3.2 II (b) Determine x1 and x2 in terms of e. (c) Determine M, where M > 0, such that |f(x) L| M. (cl) Determine N, where N