A box with a square base and open top_ must have a volume of 62500 m3. 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 1:, the length of one side of the square base. [Hintz use the volume formula to express the height of the box in terms of 99.] Simplify your formula as much as possible. A.) = [:l Next, find the derivative, A'(;z:). me: Now, calculate when the derivative equals zero, that is, when A'(a:) : 0. [Hintz multiply both sides by 332.] 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"(m). we: Evaluate A"(:1:) at the zit-value you gave above. :1