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.
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,,
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.. =)