Answer to Question #149436 in Calculus for Jia

Question

A certain factory manufactures rectangular papers. Various sizes are produced by increasing the length by 6 centimeters each second and by decreasing its width by 5 centimeters each second. At a certain instant, the length of the paper is 3 centimeters, and the width is 8 centimeters. What is the rate of change of the area of the paper at that instant?

Answer 1

Change in length per second is $\Delta L=+6cm$ and Change in width is $\Delta W=-5cm$.

At the given instant $(L,W)=(3,8)$, hence area of paper is $A_1=24cm^2$and area at next second will be $A_2=(3+6)\times (8-5)=27cm^2$ .

Change in area per second is $\Delta A=A_2-A_1=3cm^2$

Hence Rate of change of area is $3cm^2/sec$ .