# 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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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.

Step 2

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

Step 3

Now let us take the first derivati...

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