A thin rectangular sheet of flexible material is being stretched in such a way that…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A thin rectangular sheet of flexible material is being stretched in such a way that its area remains exactly 120 cm² at all times. At time t seconds the sheet’s width is w(t) cm and its length is ℓ(t) cm.
(a) Using the information given, derive an equation that relates dtdℓ to dtdw without isolating either derivative.
(b) At a particular instant the width is 6.0 cm and is decreasing at 0.40 cm/s. Calculate the corresponding rate of change of the length at that instant, indicating whether the length is increasing or decreasing, and state the units of your answer.