Originally Posted by

**minusb** Hi,

This is driving me nuts... I've put in a good few hours and still stuck.. can't seem to find much on this online either.

OK, I'm trying to draw the curve of $\displaystyle \displaystyle x^3 + 2y^3 - 5xy = 0 $

I used implicit differentiation to find

$\displaystyle \displaystyle \frac{dy}{dx} = \frac{5y - 3x^2}{6y^2-5x} $

I put this equal to zero to find critical points.. gives me

$\displaystyle \displaystyle y = \frac{3x^2}{5} $

I plug this back into the original equation to simplify to

$\displaystyle \displaystyle 27x^6 - 125x^3 = 0$ so I have $\displaystyle \displaystyle x =0, \frac {5}{3} $.

And I'm stuck (badly)

I need to find the turning points and to draw the curve.. Any help?

Thank you.