The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s. when the length is 13 cm and the width is 5 cm, how fast is the area of the rectangle increasing?
Accepted Solution
A:
L(t) = 13 + 8t ............(1) W(t) = 5 + 6t .............(2) Let the area be A. A(t) = (13 + 8t)(5 + 6t) ...(3) Expanding the brackets in (3), we get: [tex]A(t)=48t^{2}+118t+65\ ..........(4)[/tex] Differentiating A with respect to time gives: [tex]\frac{dA}{dt}=96t+118[/tex] When t = 0, the rate of change of the area of the rectangle is: [tex]\frac{dA}{dt}=118[/tex] Therefore the answer is 118 square cm per second.