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A box with a square base and open top must have a volume of 131072 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(2) = Next, find the derivative, A'(x). A'(x) = 0. (Hint: multiply both sides Now, calculate when the derivative equals zero, that is, when A'(x) by x?.] 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"(2). A"(2x) Evaluate A"(x) at the x-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A() 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.) Calculator Submit Question
A baseball team plays in a stadium that holds 54000 spectators. With the ticket price at $11 the average attendence has been 23000. When the price dropped to $10, the average attendence rose to 27000. Assume that attendence is linearly related to ticket price. What ticket price would maximize revenue? $ Calculator Submit Question