The position of a particle is given parametrically by

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

The position of a particle is given parametrically by y=f(x)y=f(x), where f′(x)>0f'(x)>0 for all xx, and x(t)=e−tx(t)=e^{-t} for t>0t>0. Which statement best describes the sign of dydt\dfrac{dy}{dt} for t>0t>0? (a) dydt>0 for all t>0\dfrac{dy}{dt}>0\text{ for all }t>0 (b) dydt<0 for all t>0\dfrac{dy}{dt}<0\text{ for all }t>0 (c) dydt=0 for all t>0\dfrac{dy}{dt}=0\text{ for all }t>0 (d) The sign of dydt\dfrac{dy}{dt} depends on f′′(x)f''(x)

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