The curve passes through the point

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

The curve

xy+\lambda=0

passes through the point

(2,\, -\dfrac{\lambda}{2})

, where

\lambda

is a non-zero real constant. (i) Calculate

\dfrac{dy}{dx}

at a general point on the curve. (ii) Determine the value of

\lambda

for which the tangent at the point with

x

-coordinate

2

has slope

3

. (iii) For the value of

\lambda

obtained in part (ii), write the equation of the corresponding tangent.