For the curve defined by

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

For the curve defined by x2y+y3=5x^2y+y^3=5, answer the following: (i) Find dydx\dfrac{dy}{dx}. (ii) Calculate the slope of the tangent to the curve at the point (1,1)(1,1). (iii) Hence obtain the equations of the tangent and the normal to the curve at this point.

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