MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
For the curve y3+x2y−4y+2x=0, examine the following points and answer each part.
(i) Identify whether the tangent at (1,1) is horizontal, vertical, or neither.
(ii) Identify whether the tangent at (0,0) is horizontal, vertical, or neither.
(iii) Write the equation of the tangent line at each point where it is horizontal or vertical.