document.write( "Question 826996: Please can you answer this question
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Algebra.Com's Answer #498375 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\"y\"\"%22%22=%22%22\"\"x%5E4-x%2B1\"
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document.write( "The graph of that is gotten by plotting\r\n" );
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document.write( "(-2,19), (-1,3), (0,1), (1,1), (2,15) \r\n" );
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document.write( "The slope of a tangent line at a point IS the derivative\r\n" );
document.write( "at that point.  So we find \"%28dy%29%2F%28dx%29\"\r\n" );
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document.write( "\"%28dy%29%2F%28dx%29\"\"%22%22=%22%22\"\"4x%5E3-1\"\r\n" );
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document.write( "Evaluate that at x=1\r\n" );
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document.write( "\"%22%22=%22%22\"\"4%281%29%5E3-1\"\"%22%22=%22%22\"\"4-1\"\"%22%22=%22%22\"\"3\"\r\n" );
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document.write( "Now we find the equation of the line with slope m=3 that\r\n" );
document.write( "goes through to point where x=1.  We must find the y-coordinate,\r\n" );
document.write( "by substituting x=1 in the original equation for the graph:\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"x%5E4-x%2B1\"\r\n" );
document.write( "\"y\"\"%22%22=%22%22\"\"1%5E4-1%2B1\"\r\n" );
document.write( "\"y\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "Use the point-slope formula:\r\n" );
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document.write( "y - y1 = m(x - x1)\r\n" );
document.write( "where (x1,y1) = (1,1)\r\n" );
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document.write( "y-1 = 3(x-1)\r\n" );
document.write( "y-1 = 3x-3\r\n" );
document.write( "  y = 3x-2    <---answer\r\n" );
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document.write( "Find the points on that tangent line (0,-2), (1,1), (2,4), (3,7)\r\n" );
document.write( "and graph it as a check to make sure it looks like it's tangent \r\n" );
document.write( "to the curve:\r\n" );
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document.write( "Edwin
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