MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
The ellipse 4x2+9y2=36 is traced in the xy-plane.
(i) Find dxdy for the ellipse.
(ii) Determine all points on the ellipse at which the tangent is horizontal.
(iii) Determine all points on the ellipse at which the tangent is vertical.
(iv) Obtain the equation of the tangent line at the point (3,0) and state whether this tangent is horizontal, vertical or neither.