Question 26217
4/10/06

..(IN YOUR CASE 8-2X)  AND WIDTH = 15-2X..(IN YOUR CASE 6-2X)..AND HEIGHT =X ...SO VOLUME V IS GIVEN BY LEMGTH*WIDTH*HEIGHT 
V=(25-2X)(15-2X)X...(IN YOUR CASE (8-2X)(6-2X)X...DOMAIN OF V IS GIVEN BY THE FACT THAT LENGTH OR WIDTH CAN NOT BE NEGATIVE...CRITICAL VALUE BEING WIDTH WE GET .... 
15-2X>0...OR....15>2X...OR....7.5>X....OR X<7.5...(IN YOUR CASE 8-2X>0...AND 6-2X>0...SO X <3)
 
RANGE.....MAXIMUM VALUE....IN YOUR CASE....
V=X(8-2X)(6-2X)=X{48-16X-12X+4X^2)=4X^3-28X^2+48X...IF YOU KNOW CALCULUS
DV/DX=12X^2-56X+48=0..OR...3X^2-14X+12=0....
X=(14+SQRT.(52))/6...OR......(7+SQRT.(13))/3...OR....(7-SQRT.13)/3
X=3.54..OR...1.13.
D2V/DX2=6X-14=- VE AT X=1.13...SO MAXIMUM VOLUME IS OBTAINED AT X=1.13'