MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
Consider the curve defined by y2=x3−x.
The point P(0,0) is under investigation.
(1) Verify that P lies on the curve.
(2) Compute dxdy in general. Evaluate your result at P and classify the tangent at P as horizontal, vertical, or neither. Provide justification for your classification.
(3) Describe, in complete sentences supported by your calculation, how the classification in part (b) affects the local behavior of the curve in a neighborhood of the origin.