Originally Posted by Burky
I checked with my teacher today and he agreed with my differentiation, so differentiating definately gives:
3x^2 +(3y^2).(dy/dx) -3y -3x.(dy/dx) = 0
--> x^2 + (y^2).dy/dx - y - x.(dy/dx) = 0
Whenever you differentiate f(y), it goes to f'(y)dy/dx, so differentating y^3 gives 3y^2 dy/dx, and when you differentiate -3xy, it goes to (-3x.dy/dx) + (-3y).
After manipulating the differentiated expression, you get:
dy/dx = (x^2 - y)/(x - y^2) = 0 where x can never be equal to y^2
which gives y = x^2 again.
This suggests that every point on this curve is a turning point, which is a load of crap.
I've never heard of this, but I haven't seen as much maths as you have either. I tried this out, but I might have screwed up.
If you keep differentiating the x term you get 3! = 6. If you put that into the first derivitive equation, you get y = 6^2 = 36, which does not agree with the first equation.
If you put it into the original expression, then y = -6.59... is the only root (using my calculator to solve that)
And I have no idea what that is telling us, but I'm sure I did that thing wrong.
