0 Question 1 v Textbook ;_' @' Videos 3: [+] A box with a square base and open top must have a volume of 186624 cm3. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of onlyr 2:, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of 22.] Simplify your formula as much as possible. A(:c) = l i Next, find the derivative, A'[m). A '[;c) = l i Now, calculate when the derivative equals zero, that is, when A (:12) = U. [Hint: multiply both sides by 11:2 -] A'(:c) = 0 when a: = We next have to make sure that this value of 2: gives a minimum value for the surface area. Let's use the second derivative test. Find A"[:c). A"(m) = |\\ i Evaluate A"(:r:) at the Liz-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(:t:] is concave up around that value, so the zero of A ' (2:) must indicate a local minimum for A(:c). (Your boss is happy now.) 0 Question 2 v Textbook @ Videos [+] For the given cost function C(x) = 12100 + 600x + x2, First, find the average cost function. Use it to find: a) The production level that will minimize the average cost b) The minimal average costX Question 4 v Textbook __' @ Videos '__' [+] Score on last try: 0 of 10 pts. See Details for more. > Next question 3 Get a similar question You can retry this question below If 2000 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume = cubic centimeters. 0 Question 5 v | Textbook E @ Videos 5 [+] A fence 12 feet tall runs parallel to a tall building at a distance of 4 ft from the building as shown in the diagram. LADDE 4ft 9 We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. [A] First, find a formula for the length of the ladder in terms of 9. (Hint: split the ladder into 2 parts.) Type theta for 9. 13(9) = i [B] Now, find the derivative, L'(6). Type theta for 9. L'(6) =l [C] Once you find the value of 6' that makes L (l?) = O, substitute that into your original function to find the length of the shortest ladder. (Give your answer wrote to 5 decimal plan's.) L(9min) %' 'feet . Question 6 v Textbook @ Videos _ [+] A farmer finds that if she plants 50 trees per acre, each tree will yield 60 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest? trees Give vour answer rounded to the nearest whole number0 Question 8 v I Textbook if (9? Videos C [+] Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Yshaped configuation. Centerville is located at [11, 0) in the Qty-plane, Springfield is at [0, 10), and Shelbyville is at (O, 10). The cable runs from Centerville to some point (at, 0) on the zit-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (:13, 0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of 9:: x) = T J We find that x) has a critical number at a: = I I To verify that f($) has a minimum at this critical number we compute the second derivative f (:13) and find that its value at the critical number is I I , a positive number. Thus the minimum length of cable needed is I I 0 Question 10 v