A box with a square base and open top must have a volume of 318028 cm^3. 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) = ______ Preview Next, find the derivative, A?(x) A'(x) = ___________ Preview Now, calculate when the derivative equals zero, that is, when A?(x) = 0. [Hint: multiply both sides by x^2.] 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''(x) = _____________ Preview 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)