Calculus: x^3+y^3=8xy. What is the equation of the tangent line at (4,4)

Question

I'm confused on the steps of solving this problem. Any help would be greatly appreciated! 

Answer 1

x³ + y³ = 8xy

 

Differentiate implicitly with respect to x:

 

3x² + 3y²(dy/dx) = 8[x(dy/dx) + y]

 

(dy/dx)[3y² - 8x] = 8y - 3x²

 

                 dy/dx = (8y - 3x²) / (3y² - 8x)

 

Slope of tangent at (4,4):  (32 - 48) / (48 - 32) = -1

 

Equation of tangent line:  y - 4 = -1(x - 4)

 

                                           y = -x+8