Question: A rectangular box (with no top face) can be formed by cutting four congruent squares from the corners of a rectangular sheet of cardboard and

A rectangular box (with no top face) can be formed by cutting four congruent squares from the corners of a rectangular sheet of cardboard and then folding up the sides, as shown in the figure at right. The volume of the resulting box depends on the size of the cutouts. For example, suppose that the original sheet of cardboard is 5 cm by 8 cm and that the four cutouts are x cm square.

(a) Find a formula for the volume V(x) of the resulting box.

(b) What is the domain of this function? What does its graph look like?

(d) Find the maximum value of V(x).

(e) Show that the equation V(x) = 18 has only one solution.

A rectangular box (with no top face) can be formed by cutting

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