1. ## Horizontal tangent

At which point is the tangent to 2x/(x + y) = y horizontal?

I found the derivative of y, which is 2y/((x+y)^2 + 2x). So if the tangent is horizontal then 2y/((1+2x)(x+y)^2)=0, right?

The only thing I can come up with is the point (0,0). Is that right?

2. Since (0,0) is NOT in the Domain, that seems like an odd answer.

Further, since your only other choices are y = 0 and x NOT 0 (zero), when there is no such point on the curve, I think you're out of luck.

No solution. You may find this result unsatisfactory.

3. Originally Posted by BrownianMan
At which point is the tangent to 2x/(x + y) = y horizontal?

I found the derivative of y, which is 2y/((x+y)^2 + 2x). So if the tangent is horizontal then 2y/((1+2x)(x+y)^2)=0, right?

The only thing I can come up with is the point (0,0). Is that right?
I advice you to look over your work again. If you graph the curve, you can see that there is no horizontal tangent line at (0,0). In fact, the point (0,0) is not even part of the domain. (If you plug (0,0) into the original equation, you get y=2x/0 which is not defined and can therefore not have a tangent, let alone a horizontal one.)

Hope I helped. If you want any more help, feel free to ask.

4. Originally Posted by TKHunny
Since (0,0) is NOT in the Domain, that seems like an odd answer.

Further, since your only other choices are y = 0 and x NOT 0 (zero), when there is no such point on the curve, I think you're out of luck.

No solution. You may find this result unsatisfactory.
Your post wasn't there when I posted. Sorry if it was repetitive. But I agree, there is no solution to the problem. If you want me to prove it, just ask.