SUBJECT: CALCULUS

1. A cardboard-box manufacturer wishes to make open boxes from square pieces of cardboard of side 12 inches by cutting equal squares from the four corners and turning up the sides. (a) If x inches is the length of the side of the square to be cut out, express the number of cubic inches in the volume of the box as a function of x. (b) What is the domain of the function? (c) Prove that the function is continuous on its domain. x in (12-2x) in (12-2x) in 2. Given a function f defined by f(x) = 4 + 3x - x2 2