A rectangle has constant area of

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

100\text{ cm}^2

. At an instant when its width is increasing, which statement best describes

\dfrac{dL}{dt}

, the rate of change of its length? (a)

\dfrac{dL}{dt}

equals zero because the area stays constant, so the sides do not change in length. (b)

\dfrac{dL}{dt}

is negative because the length must decrease to keep the area constant when the width increases. (c)

\dfrac{dL}{dt}

is positive because the rectangle is getting larger in both dimensions as the width increases. (d) The sign of

\dfrac{dL}{dt}

cannot be determined from the given information; the actual width value is needed.