A box with a square base and open top must have a volume of 500000 cm3. 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 r, the length of one side of the square base. Hint: use the volume formula to express the height of the box in terms of r.] Simplify your formula as much as possible. A(z) = Preview Next, find the derivative, A'(x). Preview 2.] Now, calculate when the derivative equals zero, that is, when A (0. Hint: multiply both sides by r A' (z) = 0 when x = We next have to make sure that this value of z gives a minimum value for the surface area. Let's use the second derivative test. Find A"(). Preview Evaluate A"() at the z-value you gave above.
