MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
The relation 4xy2−x2y=1 is considered for x near 1.
(1) Solve for all points on the curve with x=1. Provide exact values for each y–coordinate.
(2) For each point obtained in part (a), calculate the slope of the tangent line and write the corresponding tangent line in point–slope form.
(3) Using the tangent line at the point with positive y–coordinate, approximate the value of y when x=1.05. Clearly state your final approximation.