A long rectangular sheet of metal, 12 inches wide, is to be made into a rain gutter by turning up two sides so that they are perpendicular to the sheet. How many inches should be turned up to give the gutter its greatest capacity?
Greatest capacity will be achieved when the area of cross section will be maximum.
Let X be the base ,so (12-X)/2 will be the height.
Area= Base x height= X(12-X)/2
Following the maximum theory, we differentiate the area w.r.t X and equate it to zero.
d/dX of(Area)=(12-2X)/2 =0
or X=6 inches(base)
so, height= (12-6)/2 = 3 inches
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