document.write( "Question 1107273: For the curve given by 4x^2+y^2=48+2xy, show that there is a point P with x-coordinate 2 at which the line tangent to the curve at P is horizontal. \n" ); document.write( "

Algebra.Com's Answer #722294 by Fombitz(32388) $\"\"$ $\"About$

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Differentiate implicitly to find the derivative,
\n" ); document.write( " $\"dy%2Fdx=%284x-y%29%2F%28x-y%29\"$
\n" ); document.write( "Set the derivative equal to zero,
\n" ); document.write( " $\"%284x-y%29%2F%28x-y%29=0\"$
\n" ); document.write( " $\"4x-y=0\"$
\n" ); document.write( " $\"y=4x\"$
\n" ); document.write( "So when $\"x=2\"$ ,
\n" ); document.write( " $\"y=4%282%29\"$
\n" ); document.write( " $\"y=8\"$
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\n" ); document.write( "(2,8)
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\n" ); document.write( "So the tangent line is $\"y=8\"$ .
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