Homework 4 P4SolutionWhen squares of side x are cut from the

Homework 4 P4

Solution

When squares of side x are cut from the corners of a flat piece admeasuring 12 inches by 6 inches, the length and the width of the remaining part of the sides will be 12 - 2x inches and 6 -2x inches respectively. On folding the sides, a box will be formed. The volume V (x) of the box = length* width* height = (12 - 2x)(6 - 2x)x. On folding the sides, a box will be formed. The volume V (x) of the box = length* width* height = (12 - 2x)(6 - 2x)x . We know that 6 < 12 and also that for making a box, there has to be some height and some width of the box. Therefore, we must have x > 0 and 2x < 6 or, x < 3. Thus, we have the inequality 0 < x < 3. Thus, the domain of V(x) is the open interval ( 0 , 3) . If the domain of V (x) is ( a, b) , then a = 0 and b = 3.