A box with open top is to be constructed from a square piece of cardboard that is 3 feet wide by cutting out a square from each of the four corners and bending up the sides.  Find the largest volume that such a box can have. a) Draw a diagram illustrating the general situation. b) Write an expression representing the volume of the resulting box. Be sure to write this volume as a function of one variable c) What is the domain of the variable in the function above? d) Find the critical numbers for this problem. e) Find the value of the variable that produces the maximum volume. f) Find the maximum volume.

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A: Please refer to the image below

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A: Please refer the attached image for complete solution.

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