Consider the curve defined implicitly by

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

x^{2}y+y^{3}=10

. The point

(1,2)

lies on the curve. (a) Find

\dfrac{dy}{dx}

in terms of

x

and

y

. (b) Evaluate

\dfrac{dy}{dx}

at the point

(1,2)

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

(1,2)

. (d) Using the tangent line at

(1,2)

, estimate the

y

–coordinate of the point on the curve whose

x

–coordinate is

1.05

. Show all supporting calculations.