Hi I had the following question:
Find the coordinates of the stationary points of the curve with equation x^3 + y^3 - 3xy = 48 and determine their nature.
So the first derivative gives y=x^2 so the turning points are at x=2 and x= cube root of -6
Now why is that some of the points that the derivative gives don't lie on the original equation, and I have to substitute y=x^2 into the original equation?
For instance, when i want to find the nature of the turning points, I tried looking at the sign of the first deravative (rather than the second) around the stationary point, but that gives dy/dx = 0 for -2, which isnt a solution?