Question 1126649
this is V=(9-2x)(12-2x)*x
f(x)=4x^3-42x^2+108x
x domain is (0, 4.5) units inches, because x=0 has no volume and x=4.5 has no volume either.

{{{graph(300,300,-2,6,-10,100,4x^3-42x^2+108x,(9-2x)(12-2x)*x)}}}

the range requires the maximum
derivative is 12x^2-84x+108
divide by 12 and set equal to 0
x^2-7x+9=0
x=(1/2)(7+/-sqrt(13)), and only sensible root is 1.70
f(1.70)=81.872 in^3

Range is (0, 81.87), units in^3.