Asked by Calvin
Squares of side length x are removed from the 4 corners of an 11in by 8.5in piece of paper. The sides are then folded up to create an open-top box. Write a funcion that determines the volume of the box and determine the functions range. How much should be cut from the corners to determine the box's maximum volume?
Answers
Answered by
Reiny
make a sketch to see that
V = x(11-2x)(8.5 - 2x)
= x(93.5 - 39x - 4x^2)
= 93.5x - 39x^2 - 4x^3
dV/dx = 93.5 - 78x - 12x^2
= 0 for a max of V
solve for x
V = x(11-2x)(8.5 - 2x)
= x(93.5 - 39x - 4x^2)
= 93.5x - 39x^2 - 4x^3
dV/dx = 93.5 - 78x - 12x^2
= 0 for a max of V
solve for x
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