Find the equation of the tangent line to the curve x^3 + y^3 = 6xy at the point (3,3).

Question

Find the equation of the tangent line to the curve x³ + y³ = 6xy at the point (3,3).

Answer 1

or x + y = 6

Note that you can answer this problem just by seeing that x and y appear the same in the equation and that we are finding the tangent at (3,3), which has the same value of x and y; you don't even need to take any derivatives.

Answer 2

Use implicit differentiation here:

3x² + 3y²y' = 6y + 6xy'. Plug in (3,3) to get m_tan:

27 + 27y' = 18 + 18y'

y' = -1 and the equation of the tangent line is y - 3 = - (x - 3).