Mathematics

Problem

The curve given by

x^{2}y+y^{3}=4

passes through the point

(1,1)

. a. Find an explicit expression for

\dfrac{dy}{dx}

in terms of

x

and

y

. Simplify completely. b. Evaluate

\dfrac{dy}{dx}

at the point

(1,1)

. c. Determine the equation of the normal line to the curve at

(1,1)