Question 1

An open box is to be made from a square piece of cardboard,24 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).If the volume of the box is represented by $V ( x ) = x ( 24 - 2 x ) ^ { 2 }$ ,determine the domain of $V ( x )$ .  
A) $D = \{ x \mid x > 0 \}$
B) $$D = \{ x \mid 0 < x < 12 \}$$
C) $D = \{ x \mid 48 < x < 96 \}$
D) $D = \{ x \mid 0 < x < 24 \}$
E) $D = \{ x \mid 12 < x < 24 \}$

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Question 2

An open box is to be made from a square piece of cardboard,28 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function,V,in terms of x,that represents the volume of the box.  
A) $V ( x ) = - 2 x ^ { 3 } + 28 x ^ { 2 }$
B) $V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 }$
C) $V ( x ) = 4 x ^ { 3 } - 56 x ^ { 2 } + 28 x$
D) $V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 } - 28 x$
E) $V ( x ) = 4 x ^ { 3 } - 112 x ^ { 2 } + 784 x$

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Question 3

An open box is to be made from a square piece of cardboard, $66 \text { inches }$ on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).After determining the function V,in terms of x,that represents the volume of the box,use a graphing utility to estimate the dimensions that will maximize its volume.  
A) $22 ^ { \prime \prime } \times 22 ^ { \prime \prime } \times 11 ^ { \prime \prime }$
B) $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 11 ^ { \prime \prime }$
C) $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 22 ^ { \prime \prime }$
D) $33 ^ { \prime \prime } \times 33 ^ { \prime \prime } \times 22 ^ { \prime \prime }$
E) $11 ^ { \prime \prime } \times 11 ^ { \prime \prime } \times 5.5 ^ { \prime \prime }$

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Quiz 12: Polynomial Functions of Higher Degree

An open box is to be made from a square piece of cardboard,28 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below) .Determine the function,V,in terms of x,that represents the volume of the box.