An open-topped box is made from a piece of cardboard that is 16 inches by 32 inches by cutting squares of equal size from each corner and bending up the flaps (see p. 210, Figure 4.9, of Ellis/Gulick for a picture). If the side of the squares is x inches, the volume V is the function V = Ax + Bx2 + Cx + D where A = 4 B = -96 C = 512 D If we include the possibility of a volume of 0, then the largest possible value for x is 16 and the smallest possible value for x is 0 To create the box with the largest possible volume, the square must have a length inches. The largest possible volume is 788.275 cubic inches.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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An open-topped box is made from a piece of cardboard that is 16 inches by 32 inches by cutting squares of equal size from each corner and bending up the flaps (see p. 210, Figure 4.9, of Ellis/Gulick
for a picture).
If the side of the squares is x inches, the volume V is the function
V = Ax3 + Bx2 + Cx + D
where A = 4
B = -96
C = 512
D = 0
If we include the possibility of a volume of 0, then
the largest possible value for x is 16
and the smallest possible value for x is 0
To create the box with the largest possible volume, the square must have a length
inches.
The largest possible volume is 788.275
v cubic inches.
Transcribed Image Text:An open-topped box is made from a piece of cardboard that is 16 inches by 32 inches by cutting squares of equal size from each corner and bending up the flaps (see p. 210, Figure 4.9, of Ellis/Gulick for a picture). If the side of the squares is x inches, the volume V is the function V = Ax3 + Bx2 + Cx + D where A = 4 B = -96 C = 512 D = 0 If we include the possibility of a volume of 0, then the largest possible value for x is 16 and the smallest possible value for x is 0 To create the box with the largest possible volume, the square must have a length inches. The largest possible volume is 788.275 v cubic inches.
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