SOLUTION: A box is formed by cutting squares from the four corners of a 9"-wide by 12"-long sheet of paper and folding up the sides.
Let x represent the length of the side of the square cut
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Let x represent the length of the side of the square cut
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Question 1126539: A box is formed by cutting squares from the four corners of a 9"-wide by 12"-long sheet of paper and folding up the sides.
Let x represent the length of the side of the square cutout (in inches), and let V represent the volume of the box (in cubic inches).
A) Write a formula that expresses V in terms of x.
B)Suppose the function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Write a function formula for f.
C)What is the domain of f ? Enter your answer as an interval.
D)What is the range of f ? Enter your answer as an interval. Answer by josgarithmetic(39617) (Show Source):
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 domain must be .
(Range,... ...)
x for the extreme values would be and . The one for the maximum v is the left-most x.
You can use to find maximum range of v. The minimum is greater than 0.
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