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 cu
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Question 1126649: 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 Boreal(15235) (Show Source): You can put this solution on YOUR website!
this is V=(9-2x)(12-2x)*x
f(x)=4x^3-42x^2+108x
x domain is (0, 4.5) units inches, because x=0 has no volume and x=4.5 has no volume either.
the range requires the maximum
derivative is 12x^2-84x+108
divide by 12 and set equal to 0
x^2-7x+9=0
x=(1/2)(7+/-sqrt(13)), and only sensible root is 1.70
f(1.70)=81.872 in^3
Range is (0, 81.87), units in^3.
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