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 #722295 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Use implicit differentiation to find an expression for dy/dx and show that there is a value of y for which the derivative is zero when x is 2.

\n" ); document.write( " $\"4x%5E2%2By%5E2=48%2B2xy\"$

\n" ); document.write( " $\"8x%2B2y%2A%28dy%2Fdx%29+=+2x%2A%28dy%2Fdx%29%2B2y\"$
\n" ); document.write( " $\"2y%2A%28dy%2Fdx%29+-+2x%2A%28dy%2Fdx%29+=+2y-8x\"$
\n" ); document.write( " $\"%282y-2x%29%2A%28dy%2Fdx%29+=+2y-8x\"$
\n" ); document.write( " $\"dy%2Fdx+=+%282y-8x%29%2F%282y-2x%29+=+%28y-4x%29%2F%28y-x%29\"$

\n" ); document.write( "When x=2, the derivative is $\"y-8%29%2F%28y-2%29\"$ ; it is zero when y is 8.

\n" ); document.write( "The tangent to the graph at P(2,8) is horizontal. \n" ); document.write( "

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