document.write( "Question 637406: Good day tutors, I need your help with this function\r
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\n" ); document.write( "\n" ); document.write( "f(x) = -3x² + 5x \r
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Algebra.Com's Answer #401643 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
Good day tutors, I need your help with this function\r
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\n" ); document.write( "\n" ); document.write( "f(x) = -3x² + 5x \r
\n" ); document.write( "\n" ); document.write( "at the point P(-1,-8) ?
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document.write( "What you are looking for is the slope of the black line which is tangent\r\n" );
document.write( "to the parabola at the point (-1,-8)\r\n" );
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document.write( "Three ways to do it: (1) if you are beginning calculus and have not studied the\r\n" );
document.write( "power rule, (2), if you are in calculus and have studied the power rule, and\r\n" );
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document.write( "(3) if you are in algebra or pre-calculus and haven't studied any calculus. \r\n" );
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document.write( "(1) If you are in calculus but haven't studied the power rule: \r\n" );
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document.write( "f'(x) =  =  =  = \r\n" );
document.write( " =  =  = \r\n" );
document.write( "\"matrix%282%2C2%2C%0D%0Alim%2C%28++-6hx-3h%5E2+%2B5h%29%2Fh%2C%0D%0A%22h-%3E0%22%2C%22%22%29+\" =  =  = \"matrix%282%2C2%2Clim%2C++-6x-3h+%2B5%2C%0D%0A%22h-%3E0%22%2C%22%22%29+%29\" = -6x-3(0)+5 = -6x+5\r\n" );
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document.write( "f'(x) = -6x+5\r\n" );
document.write( "f'(1) = -6(-1)+5 = 6+5 = 11\r\n" );
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document.write( "(2) If you've already studied the power rule \"expr%28d%2F%28dx%29%29x%5En=nx%5E%28n-1%29\"\r\n" );
document.write( "then you can get \r\n" );
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document.write( "f'(x) = -6x+5 immediately from the power rule, as the lady above did.\r\n" );
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document.write( "f'(1) = -6(-1)+5 = 6+5 = 11\r\n" );
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document.write( "-------------------------------------------\r\n" );
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document.write( "(3) If you are studying algebra and haven't studed any calculus:\r\n" );
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document.write( "Suppose the line tangent to the graph of f(x) has the equation \r\n" );
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document.write( "y = mx + b\r\n" );
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document.write( "Write y for f(x)\r\n" );
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document.write( "y = -3x² + 5x\r\n" );
document.write( "y = mx + b\r\n" );
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document.write( "Substitute the point (-1,-8) for (x,y) in y = mx+b:\r\n" );
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document.write( "-8 = m(-1) + b\r\n" );
document.write( "-8 = -m + b\r\n" );
document.write( " m - 8 = b \r\n" );
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document.write( "Substitute m - 8 for b\r\n" );
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document.write( "y = mx + m-8\r\n" );
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document.write( "Substitute for y in\r\n" );
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document.write( "y = -3x² + 5x\r\n" );
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document.write( "mx + m-8 = -3x² + 5x\r\n" );
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document.write( "3x² + mx - 5x + m-8 = 0\r\n" );
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document.write( "3x² + (m-5)x + m-8 = 0\r\n" );
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document.write( "A line is tangent to a parabola when the solution is a root\r\n" );
document.write( "of multiblicity 2.  This happens when the discriminant\r\n" );
document.write( "B²-4AC = 0,\r\n" );
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document.write( "A=3, B =(m-5), C = m-8\r\n" );
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document.write( "Discriminant = B² - 4AC = (m-5)² - 4(3)(m-8) = m²-10m+25-12m+96 = m²+22m-121\r\n" );
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document.write( "So we set \r\n" );
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document.write( "  m²+22m-121 = 0\r\n" );
document.write( "(m-11)(m-11) = 0 \r\n" );
document.write( "           m = 11\r\n" );
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document.write( "Edwin
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