5-6

Question 5 0/1 pt 9 100 99 0 Details If 1400 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. Question Help: Message instructor Submit Question Jump to Answer Question 6 0/1 pt 9 100 99 @ Details A box with a square base and open top must have a volume of 32000 cm". 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 only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x. ] Simplify your formula as much as possible. A(x) = Next, find the derivative, A' (x). A'(x) = Now, calculate when the derivative equals zero, that is, when A' (x) = 0. [Hint: multiply both sides by a .] A'(x) = 0 when x = We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(I) = Evaluate A"(x) at the x-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A' (x) must indicate a local minimum for A(x). (Your boss is happy now.) Question Help: Video Message instructor Submit Question Jump to Answer Question 7