document.write( "Question 1209605: The domain of the function q(x) = x^4 + 8x^2 + 7x^3 is (-infty,infty). What is the range? \n" ); document.write( "
Algebra.Com's Answer #849653 by mccravyedwin(408)\"\" \"About 
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document.write( "The graph of\r\n" );
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document.write( "\"q%28x%29+=+x%5E4+%2B+8x%5E2+%2B+7x%5E3\"\r\n" );
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document.write( "\"graph%28400%2C400%2C-10%2C10%2C-100%2C100%2C+x%5E4%2B8x%5E2%2B7x%5E3%29\"\r\n" );
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document.write( "We need to find the lowest point on the graph.\r\n" );
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document.write( "We use the derivative:\r\n" );
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document.write( "\"%22q%27%28x%29%22=4x%5E3%2B16x%2B21x%5E2\"\r\n" );
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document.write( "and set it equal to 0:\r\n" );
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document.write( "\"4x%5E3%2B21x%5E2%2B16=0\"\r\n" );
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document.write( "\"x%284x%5E2%2B21x%2B16%29=0\"\r\n" );
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document.write( "\"x=0\"; \"4x%5E2%2B21x%2B16=0\"\r\n" );
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document.write( "Solve that by the quadratic formula:\r\n" );
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document.write( "\"x+=+%28-21+%2B-+sqrt%28185%29%29%2F8\"\r\n" );
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document.write( "We want the lowest value which is the leftmost minimum point, so we use\r\n" );
document.write( "the - sign\r\n" );
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document.write( "We substitute \"x+=+%28-21+-+sqrt%28185%29%29%2F8\" in\r\n" );
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document.write( "\"q%28x%29+=+x%5E4+%2B+8x%5E2+%2B+7x%5E3\"  and after much work, we get\r\n" );
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document.write( "\"%28-16571+-+1295sqrt%28185%29%29%2F125\" so the range is\r\n" );
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document.write( "Edwin
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