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 #690008 by Boreal(15235)\"\" \"About 
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y\"=12x^2-8
\n" ); document.write( "y'=4x^3-8x+C1
\n" ); document.write( "y=x^4-4x^2+C1x+C2
\n" ); document.write( "When x=4 y=256-64+4C1+C2
\n" ); document.write( "4C1+C2=0
\n" ); document.write( "The slope of the line tangent to this is perpendicular to 224y=-x+448; y=-x/224+2, and it is 224, the negative reciprocal
\n" ); document.write( "point-slope y-y1=m(x-x1) m slope (x1,y1) point
\n" ); document.write( "y-192=224(x-4)
\n" ); document.write( "y=224x-704
\n" ); document.write( "The slope of 224=4x^3-8x+C1, where x=4
\n" ); document.write( "224=256-32+C1, so C1=0, C2=0
\n" ); document.write( "The curve is x^4-4x^2, or x^2(x+2)(x-2)
\n" ); document.write( "\"graph%28300%2C300%2C-10%2C10%2C-10%2C250%2Cx%5E4-4x%5E2%2C224x-704%2C-%28x%2F224%29%2B2%29\"
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