Solve the Problem $7 \mathrm{~cm} \times 6 \mathrm{~cm}$ as the Lens Zooms in and Out, the Size

Multiple Choice

Solve the problem.
-A zoom lens in a camera makes a rectangular image on the film that is $7 \mathrm{~cm} \times 6 \mathrm{~cm}$ . As the lens zooms in and out, the size of the image changes. Find the rate at which the area of the image begins to change $(\mathrm{dA} / \mathrm{df})$ if the length of the frame changes at $0.8 \mathrm{~cm} / \mathrm{s}$ and the width of the frame changes at $0.2 \mathrm{~cm} / \mathrm{s}$ .

A) $6.8 \mathrm{~m}^{2} / \mathrm{s}$
B) $6.2 \mathrm{~m}^{2} / \mathrm{s}$
C) $\frac{7}{6} \mathrm{~m}^{2} / 2$
D) $1.0333 \mathrm{~m}^{2} / \mathrm{s}$