A curve is defined implicitly by the equation

$\displaystyle x^3 + y^3 = 6xy$

a)Using Implicit Differentiation

b)Determine the location of each point on the curve whose tangent line has a slope of -1.

what i got for a) is

$\displaystyle y' = \frac{6y-3x^2}{3y^2-6x}$

i just want get clarified if thats correct or not,

and also, how do i get the answer to b? i don't know where to start.

can anyone help?

thanks!