Question 1126539
{{{v=x(9-2x)(12-2x)}}}, volume


{{{highlight(v=2x(9-2x)(6-x))}}}

v will be positive between x at 0 and x at 6 but NOT including those boundary x values.


The zeros of v are  0, 6, and 8.5.
NO value for x at nor above 6 can be accepted; beyond 8.5 will make one of the dimensions negative.  Between 6 and 8.5 would make volume v negative.


THe <b>domain</b> must be  {{{0<x<6}}}.


(Range,...   ...)

x for the extreme values would be  {{{(7-sqrt(13))/2}}} and {{{(7+sqrt(13))/2}}}.   The one for the maximum v is the left-most x.

You can use {{{x=(7-sqrt(3))/2}}}  to find maximum  range of v.  The minimum is greater than 0.


RANGE:  ( 0, 81.87 ]

{{{0<v<=81.87}}}