document.write( "Question 118651: One number is 10 greater than the other number. Find the two numbers such that their product is a minimum. What is the product? \n" ); document.write( "

Algebra.Com's Answer #86779 by Fombitz(32388) $\"\"$ $\"About$

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Let N be the first number.
\n" ); document.write( "Then N+10 is the second number.
\n" ); document.write( "Their product is N(N+10).
\n" ); document.write( " $\"P=N%28N%2B10%29\"$
\n" ); document.write( " $\"P=N%5E2%2B10N\"$
\n" ); document.write( "To find a minimum, set the derivative of P with respect to N equal to zero.
\n" ); document.write( " $\"dP%2FdN=2N%2B10\"$
\n" ); document.write( "Now set it equal to zero.
\n" ); document.write( " $\"dP%2FdN=2N%2B10=0\"$
\n" ); document.write( " $\"2N=-10\"$
\n" ); document.write( " $\"N=-5\"$
\n" ); document.write( " $\"N%2B10=5\"$
\n" ); document.write( "Graphically, the product function N(N+10) shows the same result.
\n" ); document.write( "Here x=N and y=N(N+10).
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-100%2C+100%2C+x%5E2%2B10x%29+\"$
\n" ); document.write( "The first number is -5.
\n" ); document.write( "The second number is 5.
\n" ); document.write( "Their product is -25. \n" ); document.write( "

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