document.write( "Question 1143083: What is the least possible value of X^2-1/X^2 If x>=1 \n" ); document.write( "

Algebra.Com's Answer #763856 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "Take the derivative \r\n" );
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document.write( "     -  =  + .\r\n" );
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document.write( "In the domain x >= 1  the derivative is always positive -- so, the function monotonically grows at x >= 1.\r\n" );
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document.write( "Therefore, the minimum of the function in this domain achieves at x = 1 and is equal to\r\n" );
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document.write( "     -  = 1 - 1 = 0.\r\n" );
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document.write( "The last step in solving such exercises is to make a plot\r\n" );
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document.write( "    \r\n" );
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document.write( "            Plot y =  - \r\n" );
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document.write( "to make sure (visually) that our conclusions are correct.\r\n" );
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