document.write( "Question 1075331: The second derivative of a curve is y'' = 12x^2 − 8. The tangent to this curve at (4, 192) is perpendicular to the line x + 224y − 448 = 0. Find the equation of the curve. \n" ); document.write( "

Algebra.Com's Answer #690013 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "The slope of the line  x + 224y − 448 = 0 is found by taking the derivative\r\n" );
document.write( "implicitly             1 + 224y' - 0  = 0\r\n" );
document.write( "                                224y' = -1\r\n" );
document.write( "                                   y' =  <--- slope\r\n" );
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document.write( "Since the tangent to the curve at (4,192) has slope which is perpendicular\r\n" );
document.write( "to that, it has slope which is its negative reciprocal or +224.\r\n" );
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document.write( "So we set y' = 224, and x = 4 in\r\n" );
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document.write( "Substitution C=0 in\r\n" );
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document.write( "Since the curve passes through the point (4, 192) we substitute\r\n" );
document.write( "x=4 and y=192\r\n" );
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document.write( "So to find the equation we substitute C=0 in\r\n" );
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document.write( "Edwin

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