Mathematics

Problem

Two variables

x

and

y

depend on time

t

. At a particular instant

t=t_{0}

, measurements give

\dfrac{dx}{dt}=-4\,\mathrm{units/s}

and

\dfrac{dy}{dt}=6\,\mathrm{units/s}

. a. (i) Find the instantaneous rate of change of

y

with respect to

x

t=t_{0}

. b. (ii) Interpret the sign of this value in terms of how

y

varies as

x

changes at that instant. c. (iii) If at

t=t_{0}

the point

(x,y)

lies in the first quadrant, explain whether, immediately after

t_{0}

, the point will move towards or away from the

y

–axis.