A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 4 :32. What are the dimensions of such a rectangle with the greatest possible area? Once you have set up the problem, be sure you are using calculus to determine the critical numbers. You will be required to show that work on upcoming quizzes to get credit. A piece of cardboard measuring 13 inches by 10 inches is formed into an open-top box by cutting squares with side length m from each corner and folding up the sides. Find a formula for the volume of the box in terms of :r, W) = Find the value for :1: that will maximize the volume of the box. Be sure you are using calculus to determine this answer. You will be required to show that work on upcoming quizzes to get credit. m_ A box with an open top is to be constructed by cutting equal-sized squares out of the corners of a 14 inch by 26 inch piece of cardboard and folding up the sides. a) Let U) be the length of the sides of the cut out squares. Determine a function V that describes the volume of the finished box in terms of w. w = b) What width to would maximize the volume of the box? c) What is the maximum volume? On which of the following intervals does 3; = 1.2m + 8 have an absolute maximum value? Helpful hint: There may be more than one correct choice. Pick all of the choices that are correct. C](2,8) O(_238] C][2,8] C] It does not have an absolute maximum value on any of the intervals C][2,8) On which of the following intervals does y = (a: 1)2 13 have an absolute minimum value? Helpful hint: There may be more than one correct choice. Pick all of the choices that are correct. C] [ 6, 8) C] ( 6, 8) C] [2, 3) C] It does not have an absolute minimum value on any of the intervals C] ( 6, 8] C] (2, 8]