Mathematics

Problem

The position of a particle is given parametrically by

y=f(x)

, where

f'(x)>0

for all

x

, and

x(t)=e^{-t}

for

t>0

. Which statement best describes the sign of

\dfrac{dy}{dt}

for

t>0

? a)

\dfrac{dy}{dt}>0\text{ for all }t>0

\dfrac{dy}{dt}<0\text{ for all }t>0

\dfrac{dy}{dt}=0\text{ for all }t>0

d) The sign of

\dfrac{dy}{dt}

depends on

f''(x)