Math B/6.5
A rectagular sheet of aluminum 25 inches long by 12 inches wide is to be made into a rain gutter by folding up two longer parallel sides the same number of inches at right angles to the sheet. How many inches on each side should be folded up so that the gutter will have its greatest capacity?
A rectagular sheet of aluminum 25 inches long by 12 inches wide is to be made into a rain gutter by folding up two longer parallel sides the same number of inches at right angles to the sheet. How many inches on each side should be folded up so that the gutter will have its greatest capacity?
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v(x)=(25-2x)(12)x x= inches that should be folded
=300x-24x² to obtain the maximum volume first we find the derivative
v'(x)=300-48x now we make the derivative=0
0=300-48x
48x=300
x=300/48
x=6.25 in
=300x-24x² to obtain the maximum volume first we find the derivative
v'(x)=300-48x now we make the derivative=0
0=300-48x
48x=300
x=300/48
x=6.25 in
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