Mathematics

Problem

The curve given by

x^{2}y+y^{3}=6

is shown in the

xy

–plane. a. Differentiate the relation to obtain an explicit expression for

\dfrac{dy}{dx}

in terms of

x

and

y

. Present your final answer as a single fraction. b. Find all points on the curve where the tangent line is horizontal. Show all algebraic steps that lead to your result. c. For each point found in part (b), write an equation of the normal line in point–slope form.

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