Mathematics

Problem

The coordinates

\bigl(x(t),y(t)\bigr)

of a particle moving in the first quadrant satisfy the rectangular hyperbola

x\,y=16

for all

t

. a. (i) Find the general relation connecting

\dfrac{dx}{dt}

and

\dfrac{dy}{dt}

. b. (ii) When the particle passes through the point

(4,4)

its

x

-coordinate is increasing at the rate of

2\,\text{cm s}^{-1}

. Calculate the corresponding rate of change of the

y

-coordinate. c. (iii) Determine whether

y

is increasing or decreasing at that instant and give a brief reason.