Finding local maximum

[deisy12e]

Well, the equation is x^3+y^3=3xy

and for dy/dx I got -(x^2-y)/(y^2-x)

and the next part is...setting DY/DX = 0 which I am confused on.

After, then I have to use the results from step 2 and the original equation to find the coordinates of the local maximum of x^3+y^3=3xy

can someone PLEASE explain me this. thank you!

 

[HallsofIvy]

Well, the equation is x^3+y^3=3xy

and for dy/dx I got -(x^2-y)/(y^2-x)

and the next part is...setting DY/DX = 0 which I am confused on.

Well, that just says -(x^2- y)/(y^2- x)= 0. Nothing difficult about that- except that the solution set is not a single point but a curve.

After, then I have to use the results from step 2 and the original equation to find the coordinates of the local maximum of x^3+y^3=3xy

can someone PLEASE explain me this. thank you!

A fraction is equal to 0 if and only if its numerator is 0.