document.write( "Question 982214: Quadratic equation
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Algebra.Com's Answer #603080 by Edwin McCravy(20055) $\"\"$ $\"About$

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We observe the leading term -2x⁶. The degree is the exponent
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\n" ); document.write( "left and right behaviors are downward. Thus the function has a maximum
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document.write( "We can only answer those in reverse order. So we answer first:\r\n" );
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document.write( "We find the derivative\r\n" );
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document.write( "Set y' = 0\r\n" );
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document.write( "We divide thru by the constant -12\r\n" );
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document.write( "Factor the sum of two cubes:\r\n" );
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document.write( "The real roots are x=0, x=-2  (the third factor yields only complex roots.)\r\n" );
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document.write( "We do a first derivative test of x=0 \r\n" );
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document.write( "intervals      |   x < -2 | -2 < x < 0 | x > 0\r\n" );
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document.write( "test value t   |    -3    |     1      |   3\r\n" );
document.write( "sign of y'(t)  |     +    |     -      |   -\r\n" );
document.write( "direction      | upward   | downward   | downward\r\n" );
document.write( "                 (incr.)     (decr.)     (decr.)\r\n" );
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document.write( "At -2 there is a change from increasing (upward) to decreasing (downward) \r\n" );
document.write( "Therefore there is a relative maximum pt. at x = -2.\r\n" );
document.write( "At 0 there is no change from decreasing (downward), thus a horizontal\r\n" );
document.write( "inflection point at x=0.\r\n" );
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document.write( "There are no other critical values of the derivative, so\r\n" );
document.write( "the relative maximum pt. at x = -2, is an absolute maximum point.\r\n" );
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document.write( "Now we answer this question:\r\n" );
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\n" ); document.write( "What is the maximum value reached at x = -2.
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document.write( "We substitute in the original equation:\r\n" );
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document.write( "So the maximum value is 10.  Observe the maximum point (-2,10),\r\n" );
document.write( "and also the horizontal inflection point at (0,-118)\r\n" );
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document.write( "Edwin

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