An open box is to be made from a flat piece of material 18 inches long and 2 inches wide by cutting equal squares of length xfrom the corners and folding up the sides.

Question

Write the volume Vof the box as a function of x. Leave it as a product of factors, do not multiply out the factors.
V=

If we write the domain of the box as an open interval in the form (a,b), then what is a=?
a=
and what is b=?

I got V=x(18-2x)(2-2x)
and a=0
b=9

but it says that its not correct

Answer 1

Your equation V=x(18-2x)(2-2x) , which is correct, describes the volume for any given x

clearly V has to be a positive number.
notice that for x=9 and x=1, V is zero.

for all values of x between 1 and 9 , V is positive,
for x<1 and x > 9 , V is negative.
try a number between 1 and 9

Draw your conclusion from my hints.

Answer 2

the equation you got is correct,, =)
first, note that x (which is the height of the box) cannot be negative, since there is no negative height,,
equating V to zero,
x=0, 1, 9

now, get some values in between (and if you want, get also a value greater than 9), and check if the dimensions will all be positive, and V will be positive as well,,
example,,
if x = 0.5, V = (0.5)(17)(1) = 8.5
if x = 4, V = (4)(10)(-6) = -240
if x = 10, V = (10)(-2)(-18) = 360

note that even if the volume that we got for x = 10 is positive, the length and width are negative, which cannot happen,,
therefore, domain is (0,1)

so there,, i hope i was able to help.. =)