document.write( "Question 988985: The second number is the reciprocal of the first number and the sum is the minimum. \n" ); document.write( "

Algebra.Com's Answer #609441 by KMST(5328) $\"\"$ $\"About$

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$\"x\"$ = the first number, so
\n" ); document.write( " $\"1%2Fx\"$ = the second number = the reciprocal of the first number, and
\n" ); document.write( " $\"S=x%2B1%2Fx\"$ = the sum.
\n" ); document.write( "The derivative is
\n" ); document.write( " $\"dS%2Fdx=1-1%2Fx%5E2=%28x%5E2-1%29%2Fx%5E2=%28x%2B1%29%28x-1%29%2Fx%5E2\"$
\n" ); document.write( " $\"dS%2Fdx\"$ is positive for $\"x%3C-1\"$ , meaning that $\"S\"$ is increasing in $\"%22%28%22\"$ $\"-infinity\"$ $\"%22%2C%22\"$ $\"-1\"$ $\"%22%29%22\"$ .
\n" ); document.write( " $\"dS%2Fdx\"$ is negative for $\"-1%3Cx%3C1\"$ , meaning that $\"S\"$ is decreasing in $\"%22%28%22\"$ $\"-1\"$ $\"%22%2C%22\"$ $\"1\"$ $\"%22%29%22\"$ .
\n" ); document.write( " $\"dS%2Fdx=0\"$ for $\"x=-1\"$ , where $\"S\"$ has a maximum.
\n" ); document.write( " $\"dS%2Fdx\"$ is positive for $\"x%3E1\"$ , meaning that $\"S\"$ is increasing in $\"%22%28%22\"$ $\"1\"$ $\"%22%2C%22\"$ $\"infinity\"$ $\"%22%29%22\"$ .
\n" ); document.write( " $\"dS%2Fdx=0\"$ for $\"highlight%28x=1%29\"$ , where $\"S\"$ has a minimum. \n" ); document.write( "

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