(286) Hindi Af Somali Cusub 202 x MOER X New Tab X + C moer.maricopa.edu/assess2/?cid=131628laid=964509#/skip/5 A box with a square base and open top must have a volume of 78732 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 a, 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' (a) = 0. [Hint: multiply both sides by x2 . ] A' (a) = 0 when ac = We next have to make sure that this value of a gives a minimum value for the surface area. Let's use the second derivative test. Find A"(a). A" (a ) = Evaluate A"(x) at the a-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(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.) hp X N o w 9 P