document.write( "Question 1200312: Assume that f(x) is continuous everywhere and
\n" ); document.write( "lim (as x approaches to 4) (f(x)+2)/(x-4) = 11\r
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Algebra.Com's Answer #834433 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "The question is badly worded, because unless a continuous function is a linear\r\n" );
document.write( "function, there are infinitely many tangent lines, not just one tangent line as\r\n" );
document.write( "the words \"the tangent line\" here seems to imply.\r\n" );
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document.write( "The question should be:\r\n" );
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document.write( "\"From the given information, is there a point at which we can determine the\r\n" );
document.write( "equation of the tangent line? If so what is that point and what is the equation\r\n" );
document.write( "of the tangent line at that point.\"\r\n" );
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document.write( "Since the denominator is 0 when x=4, the numerator must also = 0 when x=4.\r\n" );
document.write( "Therefore,\r\n" );
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document.write( "f(4)+2 = 0\r\n" );
document.write( "  f(4) = -2\r\n" );
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document.write( "Therefore, we know that (4,-2) is a point on f(x).\r\n" );
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document.write( "Since both the numerator and denominator of  both\r\n" );
document.write( "approach 0 as x approaches 4, we know that L'Hopital's rule holds.  Therefore\r\n" );
document.write( "the quotient of the derivatives of the numerator and denominator has the same\r\n" );
document.write( "limit 11 as x approaches 4.\r\n" );
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document.write( "Therefore, f'(4) = 11, the slope of a tangent line at (4,-2)\r\n" );
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document.write( "So we know that at the point (4,-2) the slope of the tangent line is 11.\r\n" );
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document.write( "Using the point-slope formula for the equation of a line:\r\n" );
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document.write( " is the equation of the tangent line to\r\n" );
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document.write( "f(x) at the point (4,-2)\r\n" );
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document.write( "Edwin

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