Answer to Question #4842 in Calculus for Liliana Chavez
A. What is the length of the side of the square cut out from the corners of the box. Let x = the length of the side of the square cut out of the corners
B. What is the maximum volume of such a box?
Let's find the derivative of volume with respect to x: V' = 12x^2-80x+100. Let's consider equation 12x^2-80x+100 = 0. It has two solutions: x=5, which turns V(x) to zero and x=5/3, which turns V(x) to maximum. So, maximum volume of the box is V(5/3) = 10000/135.
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