document.write( "Question 1023927: Find two points on the curve
\n" ); document.write( "(C)렁렁렁 x^2 y+y^4 +6=4+2x,
\n" ); document.write( "where x = 1. At each of those points , find an equation of the tangent line to C. \n" ); document.write( "

Algebra.Com's Answer #639439 by Fombitz(32388) $\"\"$ $\"About$

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\n" ); document.write( " $\"%281%29%5E2y%2By%5E4%2B6=4%2B2%281%29\"$
\n" ); document.write( " $\"y%2By%5E4=0\"$
\n" ); document.write( " $\"%28y%5E3%2B1%29y=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"y=0\"$
\n" ); document.write( "and
\n" ); document.write( " $\"y%5E3%2B1=0\"$
\n" ); document.write( " $\"%28y%2B1%29%28y%5E2-y%2B1%29=0\"$
\n" ); document.write( " $\"y=-1\"$
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\n" ); document.write( "To find the slope of the tangent line, find the derivative at that point.
\n" ); document.write( "Differentiate implicitly,
\n" ); document.write( " $\"x%5E2dy%2By%282xdx%29%2B4y%5E3dy=2dx\"$
\n" ); document.write( " $\"%28x%5E2%2B4y%5E3%29dy=%282-2xy%29dx\"$
\n" ); document.write( " $\"dy%2Fdx=%282-2xy%29%2F%28x%5E2%2B4y%5E3%29\"$
\n" ); document.write( "When $\"x=1\"$ , $\"y=0\"$ ,
\n" ); document.write( " $\"m=dy%2Fdx=%282-0%29%2F%281%2B0%29=2\"$
\n" ); document.write( "So then the tangent line is,
\n" ); document.write( " $\"y-0=2%28x-1%29\"$
\n" ); document.write( " $\"y=2x-2\"$
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\n" ); document.write( "When $\"x=1\"$ , $\"y=-1\"$ ,
\n" ); document.write( " $\"m=dy%2Fdx=%282-2%281%29%28-1%29%29%2F%281-4%29=-4%2F3\"$
\n" ); document.write( "So then the tangent line is,
\n" ); document.write( " $\"y%2B1=%28-4%2F3%29%28x-1%29\"$
\n" ); document.write( " $\"y=-%284%2F3%29x%2B4%2F3-3%2F3\"$
\n" ); document.write( " $\"y=-%284%2F3%29x%2B1%2F3\"$
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.\r
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