Mathematics

Problem

For the curve given by

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

and

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

(

t\ne0

), answer the following. a. (i) Compute

\dfrac{dy}{dx}

in terms of

t

. b. (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. c. (iii) Determine the corresponding point(s) on the curve and find the equation of the tangent at each such point.

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