document.write( "Question 1153034: Find the equation of the tangent to the curve x^2y-x=y^3-8 at x=0. \n" ); document.write( "

Algebra.Com's Answer #775193 by Edwin McCravy(20060) $\"\"$ $\"About$

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x^2y-x=y^3-8 at x=0
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document.write( "Substituting x=0,\r\n" );
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document.write( "So the point of tangency is (0,2), and we want the equation of the\r\n" );
document.write( "green line below:\r\n" );
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document.write( "We find the slope of the tangent line, which is the\r\n" );
document.write( "same as the derivative at that point:  So we find\r\n" );
document.write( "the derivative implicitly, i.e., without solving for\r\n" );
document.write( "the independent variable y:\r\n" );
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document.write( "We substitute x=0 and y=2 and solve for \r\n" );
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document.write( "That's the slope of the tangent line at (0,2), which is\r\n" );
document.write( "the green line. So\r\n" );
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document.write( "Since the point of tangency is the y-intercept (0,2), we can just\r\n" );
document.write( "use:\r\n" );
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document.write( "with \r\n" );
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document.write( "Edwin

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