A box with a square base and open top must have a volume of 171500 cm. We wish to find the dimensions of the box that mi

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A Box With A Square Base And Open Top Must Have A Volume Of 171500 Cm We Wish To Find The Dimensions Of The Box That Mi 1 (37.04 KiB) Viewed 18 times

A box with a square base and open top must have a volume of 171500 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 c.] Simplify your formula as much as possible. A(x) = Next, find the derivative, A'(x). A'(:) Now, calculate when the derivative equals zero, that is, when A'(x) = 0. (Hint: multiply both sides by <?) A'(x) = 0 when 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"(x). A"(x) Evaluate A"(x) at the r-value you gave above.