Let where and vary with time

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Let

y=4x^{3}-3x+2

where

x

and

y

vary with time

t

. At the instant when

x=1\,\mathrm{cm}

, the quantity

y

is observed to be changing at

5\,\mathrm{cm\,s^{-1}}

. Determine the corresponding rate of change of

x

. (i) Compute

\dfrac{dy}{dx}

x=1

. (ii) Hence calculate

\dfrac{dx}{dt}

at that instant, stating the appropriate unit.