document.write( "Question 1052786: Find the nature of the stationery points of the curve xy+ 64x^2+1=0 and the coordinates of these points \n" ); document.write( "

Algebra.Com's Answer #668289 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "Find the nature of the stationery points of the curve xy+ 64x^2+1=0 and the coordinates of these points
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document.write( "Your curve is\r\n" );
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document.write( "y = -,  or, which is the same, y = .\r\n" );
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document.write( "First derivative is\r\n" );
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document.write( " =  + \r\n" );
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document.write( "The first derivative has a zero at\r\n" );
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document.write( " = 64,   or   x = +/-.\r\n" );
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document.write( "There are two stationery points. One is (,). The other is (,).\r\n" );
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document.write( "           Plot y = \r\n" );
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document.write( "The function is an odd function and has two branches.\r\n" );
document.write( "The branch in the second quarter is convex downward.\r\n" );
document.write( "The branch in the fourth quarter is convex upward.\r\n" );
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document.write( "On terminology see this Wikipedia article.\r\n" );
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