document.write( "Question 858571: This is a calculus problem. Consider two integers x and y such that x−y=12. What value of y will minimize x^2+y^2? \n" ); document.write( "

Algebra.Com's Answer #517372 by Fombitz(32388) $\"\"$ $\"About$

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$\"L=x%5E2%2By%5E2\"$
\n" ); document.write( "Substitute,
\n" ); document.write( " $\"x-y=12\"$
\n" ); document.write( " $\"x=12%2By\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"L=%2812%2By%29%5E2%2By%5E2\"$
\n" ); document.write( " $\"L=%28144%2B24y%2By%5E2%29%2By%5E2\"$
\n" ); document.write( " $\"L=2y%5E2%2B24y%2B144\"$
\n" ); document.write( "Take the derivative of L with respect to y and set it to zero.
\n" ); document.write( " $\"dL%2Fdy=4y%2B24=0\"$
\n" ); document.write( " $\"4y%2B24=0\"$
\n" ); document.write( " $\"4y=-24\"$
\n" ); document.write( " $\"y=-6\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"x=12-6\"$
\n" ); document.write( " $\"x=6\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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