see the details.?

Question

**An open-topped box is made from a piece of cardboard that is 24 inches by 34 inches by cutting squares of equal size from each corner and bending up the flaps (see p. 213 for a picture).

Find a function that models the volume V in terms of the length of a side x of the squares.

V(x) = x3 + x2 + x + (cubic inches)

The largest possible value for x is .
The smallest possible value for x is .

Answer 1

this should help http://mathforum.org/library/drmath/sets/select/dm_box_maxvol.html

Answer 2

the volume of the box is going to be the area of the base times the height. we know the height is going to be x. the area of the base is length times width. Because we started with a 24x34 piece of cardboard and removed 2x from each dimension (one x from each side) we know that the length and width of the base are going to be 24-2x and 34-2x so the volume of the box is going to be (24-2x)(34-2x)x = (816-116x+4x²)x = 4x³-116x²+816x. the smallest and largest possible value will be bounded by 0 and 12 but 0 and 12 are themselves unrealistic values for x since they won't yield a box but anything in between them works (theoretically) so the possible values for x can be written as 0

Answer 3

I was all set to help you but then I saw the equation you provided. I think you meant for it to be a power series which should have been typed: V(x) = x^3 + x^2 + x + (cu. in.)

Where did you get that equation? I can't imagine how it could be related to the question you've asked. Rather than lead you astray with my own opinion (the same as "snilubez" above), I've chosen not to answer. Hopefully, someone else who understands your expectations will come along. Advice -- when asking technical questions, don't add details you're not absolutely certain are correct. I'm here to solve math problems, not to fulfill your numerical expectations, and there's no way for me to ask what's a fact and what's just a guess. Good Luck...................