Find all points on the curvex^2y^2+ xy = 2

where the slope of the tangent line is -1.

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- Dec 3rd 2007, 05:39 PMsingh1030implicit differentiationFind all points on the curvex^2y^2+ xy = 2

where the slope of the tangent line is -1.

- Dec 3rd 2007, 06:03 PMJhevon
- Dec 3rd 2007, 06:05 PMsingh1030
yea i did sorry

- Dec 3rd 2007, 06:12 PMJhevon
just remember to attach y' = dy/dx when you differentiate a y-term, since you are taking the derivative of y with respect to x. when we are taking the derivative of an x-term, we don't have to attach anything, since we would have dx/dx which cancels to 1. also note that we differentiate xy by the product rule

$\displaystyle x^2 + y^2 + xy = 2$

$\displaystyle \Rightarrow 2x + 2y~y' + y + x~y' = 0$

we want the slope to be -1, so set $\displaystyle y' = -1$ and solve for the resulting function