document.write( "Question 1199429: What is the smallest possible value of the multivariable function \r
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Algebra.Com's Answer #833306 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "    f(x,y) = 2x^2 + y^2 - 2xy + 6x - 1 = re-group = x^2 + (x^2 -2xy + y^2) + 6x - 1 = \r\n" );
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document.write( "  = (x^2 + 6x - 1) + (x-y)^2 = (x^2 + 2*3x + 9) - 10 + (x-y)^2 = (x+3)^2 + (x-y)^2 - 10.\r\n" );
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document.write( "From this expression for  f(x,y)  it is seen that the minimum of  f(x,y)  is when\r\n" );
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document.write( "    x = -3, y = -3.\r\n" );
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document.write( "Indeed, then both the quadratic terms  (x+3)^2  and  (x-y)^2  achieve their minimum possible \r\n" );
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document.write( "values of zero simultaneously, and the minimum value of  f(x,y)  is  -10.    ANSWER\r\n" );
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