Answer:
V = 4x^3-39x^2+93.5x
Domain: 0 < x < 4.25
Using the graph the maximum volume is about V = 66 inches ^3 at about x = 1.6
Step-by-step explanation:
V = l*w*h
The length is 11 -2x
The width is 8.5 -2x
The height is x
V = ( 11 -2x) ( 8.5 -2x) x
FOIL ( first outer inner last)
V = (93.5 -22x - 17x +4x^2) x
Combine like terms
V =( 4x^2-39x+93.5)x
Distribute the x
V = 4x^3-39x^2+93.5x
The domain is the values that x can take
Looking at the picture
2x can be no largest than 8.5 or there will be no width
2x < 8.5
x < 4.25
If x ≤ 0 there is no height so x > 0
0 < x < 4.25
Using the graph the maximum volume is about V = 66 inches ^3 at about x = 1.6
