document.write( "Question 1051078: maximize q=5xy^2, where x and y are positive numbers such that x+y^2=8 \n" ); document.write( "

Algebra.Com's Answer #666663 by Fombitz(32388) $\"\"$ $\"About$

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$\"x=8-y%5E2\"$
\n" ); document.write( "Substitute into q equation,
\n" ); document.write( " $\"q=5%288-y%5E2%29y%5E2\"$
\n" ); document.write( "Now q is a function of one variable, y.
\n" ); document.write( "To find the maximum, differentiate with respect to y and set the derivative equal to zero.
\n" ); document.write( " $\"dq%2Fdy=5%288-y%5E2%29%282y%29%2B5%28y%5E2%29%28-2y%29\"$
\n" ); document.write( " $\"dq%2Fdy=80y-10y%5E3-10y%5E3\"$
\n" ); document.write( " $\"dq%2Fdy=80y-20y%5E3\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"80y=20y%5E3\"$
\n" ); document.write( " $\"y%5E2=4\"$
\n" ); document.write( "Remember y is positive,
\n" ); document.write( " $\"y=2\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"x%2B2%5E2=8\"$
\n" ); document.write( " $\"x%2B4=8\"$
\n" ); document.write( " $\"x=4\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"q%5Bmax%5D=5%284%29%284%29=80\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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