3.9 Related Rates

Question

The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 11 cm and the width is 6 cm, how fast is the area of the rectangle increasing (in cm²/s)?

 cm²/s

Answer 1

L' = 3 , L=11

w' = 7 w=6

A= Lw

A' = Lw' + wL' = 77 +18

= 95 cm^2/sec

= the Area's instantaneous rate of change

check the answer

in one second it increased from 66 to 14(13) = 182, an increase of 116

one second earlier it increased from -8 to 66 an increase of 74

average of 74 and 116= 190/2 = 95 cm^2/sec = the average Area's rate of change= the Area's instantaneous rate of change