Thread: Need help with implicit differentiation!

1. Need help with implicit differentiation!

Well, it's not so much the differentiating I need help with. we have this (2x-x^2y^2=4y-4) formula, and need to use implicit differentiation to find the leftmost point of the graph. figured out that dy/dx = (1-xy^2)/(2-x^2y), guessing I need solve it equal to 0.

Tried solving dy/dx = 0, got y=+/- sqrt(x-1) and tried substituting it into the original formula but that was incorrect. I'm stuck!

2. Re: Need help with implicit differentiation!

dy/dx = 0? Why would that help you find a VERTICAL asymptote? Try dx/dy.

3. Re: Need help with implicit differentiation!

Originally Posted by TKHunny
dy/dx = 0? Why would that help you find a VERTICAL asymptote? Try dx/dy.
Well you might aswell find dy/dx, and see where its not defined since dx/dy is the reciprocal of dy/dx

4. Re: Need help with implicit differentiation!

What's the difference? Anyway, one should also be sure of two other things, besides dx/dy = 0:

1) dy/dx is not also zero, and
2) dx/dy doesn't have some other value as well as zero.

We are looking for a left-most point.

5. Re: Need help with implicit differentiation!

$\frac{dy}{dx}=0\Rightarrow y=\pm \sqrt{\frac{1}{x}}$
not $\pm \sqrt{x-1}$ !!!!!!!!