A box is formed by cutting squares from the four corners of a 11"-wide by 13"-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.V = x(11-2x) (13-2x)Previewb. Suppose the function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Write a function formula forf.f(x)Previewx(11-2x) (13-2x)c. What is the domain of f? Enter your answer as an interval. Hint.Preview[0,11/2]d. What is the range of f? Enter your answer as an interval. HintTip: Use a graphing tool like www.Desmos.com to find the maximum volume possible.[0, oo) [0,00)Preview[0,00)

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Asked Oct 24, 2019
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A box is formed by cutting squares from the four corners of a 11"-wide by 13"-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.
V = x(11-2x) (13-2x)
Preview
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.
f(x)
Preview
x(11-2x) (13-2x)
c. What is the domain of f? Enter your answer as an interval. Hint.
Preview
[0,11/2]
d. What is the range of f? Enter your answer as an interval. Hint
Tip: Use a graphing tool like www.Desmos.com to find the maximum volume possible.
[0, oo) [0,00)
Preview
[0,00)
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A box is formed by cutting squares from the four corners of a 11"-wide by 13"-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. V = x(11-2x) (13-2x) Preview 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. f(x) Preview x(11-2x) (13-2x) c. What is the domain of f? Enter your answer as an interval. Hint. Preview [0,11/2] d. What is the range of f? Enter your answer as an interval. Hint Tip: Use a graphing tool like www.Desmos.com to find the maximum volume possible. [0, oo) [0,00) Preview [0,00)

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Step 1

Given that a box is formed by cutting squares from the four corners. If x is the length of side cut out (in inches) and V represents the volume of the box.

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Now, the function that represents V in terms of x is f(x) — x(11 — 2х)(13 — 2х) To Find: The Range of the function f,

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Step 2

We find the range by finding the value of x such that the volume is maximum. Expanding the equation and simplifying gives,

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f(х) — (11х — 2x?)(13 — 2х) - 13(11x - 2x2)- 2x(11x - 2x2 — 13(11х — 2x?) — 2х(11х — 2х?) 4x3 — 48х2 + 143х

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Step 3

Now let us take the first derivati...

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df 12x2 96x 143 dx Setting the first derivative equal to zero and solving for the roots will give the critical points. 12x2 96x 143 = 0

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Algebra

Equations and In-equations