document.write( "Question 541160: from a square sheet of cardboard 40 cm by 40 cm, square corners are cut out so the sides can be folded up to make a box. what dimensions will yield a box of max. volume? \n" ); document.write( "
Algebra.Com's Answer #354088 by lwsshak3(11628)\"\" \"About 
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from a square sheet of cardboard 40 cm by 40 cm, square corners are cut out so the sides can be folded up to make a box. what dimensions will yield a box of max. volume?
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\n" ); document.write( "let x = sides (cm) of square corners cut out
\n" ); document.write( "40-2x=sides (cm) of bottom of box
\n" ); document.write( "(40-2x)^2=area of bottom of box
\n" ); document.write( "volume of box=x(40-2x)^2=x(1600-160x+4x^2)
\n" ); document.write( "f(x)=4x^3-160x^2+1600x
\n" ); document.write( "Normally, I don't do calculus problems, but this one is a max/min problem which requires calculus for an answer. To find the maximum volume, you must take the first derivative of the function, set it equal to zero, then solve for x:
\n" ); document.write( "..
\n" ); document.write( "f(x)=4x^3-160x^2+1600x
\n" ); document.write( "f'(x)=12x^2-320x+1600=0
\n" ); document.write( "3x^2-80x+400=0
\n" ); document.write( "(3x-20)(x-20)=0
\n" ); document.write( "..
\n" ); document.write( "3x-20=0
\n" ); document.write( "x=20/3
\n" ); document.write( "or
\n" ); document.write( "x-20=0
\n" ); document.write( "x=20
\n" ); document.write( "number line for critical points of derivative:
\n" ); document.write( "<....+...20/3.....-.....20......+........>
\n" ); document.write( "max at x=20/3 and min at x=20
\n" ); document.write( "Ans:
\n" ); document.write( "To yield a box of max. volume, sides of square cut outs should=20/3 cm \n" ); document.write( "
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