The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 5 cm/s. when the length is 13 cm and the width is 11 cm, how fast is the area of the rectangle increasing?
A = xy A' = xy' +x'y A' = (13 cm)*(5 cm/s) +(8 cm/s)*(11 cm) .. = (65 +88) cm^2/s .. = 153 cm^2/s . . . . . . . the rate at which rectangle area is changing
_____ Check: .005 seconds before the time of interest, the area was .. (13 cm -.005*8 cm) * (11 cm -.005*5 cm) = 12.96*10.975 = 142.236 cm^2 .005 seconds after the time of interest, the area is .. 13.04* 11.025 = 143.766 cm^2 So the average rate of change over that 0.01 second interval is .. (143.766 -142.236)/(.01) = 153 cm^2/s . . . . close enough
