For the curve given by and ( )

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

Problem

For the curve given by

x=t+\dfrac{1}{t}

and

y=t-\dfrac{1}{t}

(

t\ne0

), answer the following. (i) Compute

\dfrac{dy}{dx}

in terms of

t

. (ii) Find all value(s) of

t

for which the tangent has slope

-1

, under the additional condition that the

x

-coordinate of the point is positive. (iii) Determine the corresponding point(s) on the curve and find the equation of the tangent at each such point.

Related theory

Straight Lines
Advanced Differentiation
Implicit and parametric differentiation
Derivatives of parametric functions
Continuity and Differentiability

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