SOLUTION: A box is to be constructed from a sheet of cardboard that is 10 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides. What is the maxim

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Question 1053912: A box is to be constructed from a sheet of cardboard that is 10 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides.
What is the maximum volume this box could have? (Round your answer to two decimal places.)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Height would be x.
The other two dimensions are (10-2x) and (50-2x).

v%28x%29=x%2810-2x%29%2850-2x%29
v%28x%29=4x%285-x%29%2825-x%29
v%28x%29=4x%28125-30x%2Bx%5E2%29
v%28x%29=500x-120x%5E2%2B4x%5E3

Instead of continuing steps to solve, what you would do next is dv/dx, equate dv/dx=0, and find x. Figure if this is a or are max or min.