Find the slope of the tangent line to the curve − 2x^2 + 2xy − 3y^3 = 85 at the point ( − 1 , − 3 ) .

Answer 1

the derivative is

4x + 2xy' + 2y - 8y^2 y' = 0

4(-1) + 2(-1) y' + 2(-3) - 8(-3)^2 y' = 0

-4 + -2y' + -6 - 72y' = 0

-74y' + -10 = 0

y' = -10/74 = -5/37