If a box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by the function , where x is the length of each side of the cross section (in inches). What restrictions must be placed on x (the domain) so that the volume makes physical sense?

Question

If a box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by the function  , where x is the length of each side of the cross section (in inches). What restrictions must be placed on x (the domain) so that the volume makes physical sense? ​

Quizplus · Accepted Answer

The volume of the box cannot be negative or zero, so we need to ensure that the function 11ea984b_af9d_1d9d_9029_59c25370b91b_TB4005_11 is positive. Thus, we solve for x: 11ea984b_af9d_1d9d_9029_59c25370b91b_TB4005_11 > 0 (x^2)^2(66-x) > 0 Since x^2 and (66-x) are both nonnegative for all real x, we only need to worry about the first factor, which is x^2. This means that x^2 > 0, so x can be any non-zero real number. However, we also need to ensure that the length of each side of the cross section is less than or equal to 66 inches, so the final answer is 0 < x < 22.

If a Box with a Square Cross Section Is to Be