1. (Maximum Open Box from a Square): Suppose that we have a 6" ( times 6 ) " sheet of paper that we are going to use to create a box with an open top by cutting squares at each corner and folding up. a) Express the volume of the box in terms of ( x ). b) Use calculus to find the maximum possible volume of such a box. 2. Write your own proble

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1. (Maximum Open Box from a Square): Suppose that we have a 6&#34;  (  times 6  ) &#34; sheet of paper that we are going to use to create a box with an open top by cutting squares at each corner and folding up. a) Express the volume of the box in terms of  ( x  ). b) Use calculus to find the maximum possible volume of such a box. 2. Write your own problem similar to this one, but starting with a non square rectangular sheet of some size. Solve your problem with calculus.

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