document.write( "Question 1093081: The tangent line to a function f(x) at x=4 is found to be y = -5x+6.
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Algebra.Com's Answer #707749 by Edwin McCravy(20055)\"\" \"About 
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The tangent line to a function f(x) at x=4 is found to be y= -5x+6.
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document.write( "Since the point of tangency is on both f(x) and the tangent line,\r\n" );
document.write( "and since when x=4, the tangent line and x=4 has y value \r\n" );
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document.write( "y = -5(4)+6 = -20+6 = -14, \r\n" );
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document.write( "then (4,-14) the point on tangency is a point on the \r\n" );
document.write( "graph of f(x).  That is,\r\n" );
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document.write( "f(4) = -14 \r\n" );
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document.write( "Since f'(4) is the slope of the tangent line at x=4, and the tangent\r\n" );
document.write( "line is y = -5x+6 which has slope -5 (which is found either by \r\n" );
document.write( "comparing it to y = mx+b, or by finding \"dy%2Fdx=-5\"). \r\n" );
document.write( "then f'(4) = 5\r\n" );
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document.write( "g(x) = 2f(x)+8\r\n" );
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document.write( "so\r\n" );
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document.write( "g(4) = 2f(4)+8\r\n" );
document.write( "g(4) = 2(-14)+8\r\n" );
document.write( "g(4) = -28+8\r\n" );
document.write( "g(4) = -20\r\n" );
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document.write( "Since \r\n" );
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document.write( "g(x) = 2f(x)+8,\r\n" );
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document.write( "taking the derivative of both sides:\r\n" );
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document.write( "g'(x) = 2f'(x)\r\n" );
document.write( "g'(4) = 2f'(4)\r\n" );
document.write( "g'(4) = 2(5)\r\n" );
document.write( "g'(4) = 10\r\n" );
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document.write( "Edwin
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