How do you find the slope of a tangent line to the graph of the function #x^3 + y^3 – 6xy = 0#, at (4/3, 8/3)? Calculus Derivatives Tangent Line to a Curve 1 Answer Timber Lin Apr 5, 2018 #4/5# Explanation: use implicit differentiation #d/dx(x^3+y^3-6xy)=d/dx(0)# #3x^2+3y^2*(dy)/dx-6(1)y-6x*(dy)/dx=0# solve for #(dy)/dx#, which gives the tangent slope at point #(x,y)# #3y^2*(dy)/dx-6x*(dy)/dx=-3x^2+6y# #(dy)/dx(3y^2-6x)=-3x^2+6y# #(dy)/dx=(-3x^2+6y)/(3y^2-6x)# plug in #(4/3,8/3)#: #(dy)/dx# at #(4/3,8/3) =(-3(4/3)^2+6(8/3))/(3(8/3)^2-6(4/3))# #(dy)/dx# at #(4/3,8/3) =(-16/3+16)/(64/3-8)# #(dy)/dx# at #(4/3,8/3) =(32/3)/(40/3)# #(dy)/dx# at #(4/3,8/3) =4/5# Answer link Related questions How do you find the equation of a tangent line to a curve? How do you find the slope of the tangent line to a curve at a point? How do you find the tangent line to the curve #y=x^3-9x# at the point where #x=1#? How do you know if a line is tangent to a curve? How do you show a line is a tangent to a curve? How do you find the Tangent line to a curve by implicit differentiation? What is the slope of a line tangent to the curve #3y^2-2x^2=1#? How does tangent slope relate to the slope of a line? What is the slope of a horizontal tangent line? How do you find the slope of a tangent line using secant lines? See all questions in Tangent Line to a Curve Impact of this question 14057 views around the world You can reuse this answer Creative Commons License