A rectangular piece of tin has an area of 1334 square inches. A square tab of 3 inches is cut from
each corner, and the ends and sides are turned up to make an open box. If the volume of the box is
2760 cubic inches, what were the original dimensions of the rectangular piece of tin? Show the work
that leads to the answer.
Find and simplify the difference quotient of y = V(x). That is, find (௫ା)ି(௫)
. (This will get a little
messy.) Then, substitute h with 0 and simplify. The expression you obtained is called the derivative of
y = V(x). (You will study derivatives in calculus.) Now, find the zeros of the derivative accurate to three
decimal places. What do you notice?