Q12 of 45 Page 1

The length x, of a rectangle, is decreasing at the rate of 5 cm/minute and the width y, is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rate of change of the area of the rectangle.

In the problems of rates in the application of derivates always look at the units of rates given, in this question the rates have units of distance/time.

= - 5 cm/minute, = + 4 cm/minute, (at x = 8, y = 6) = ?


There are two sides of rectangle x and y, so the area of the rectangle will be A = xy, and we have to calculate the rate of change of area with time.


A = x y


Differentiating both sides,



= 6( - 5) + 8(4) = - 30 + 32 = 2 cm2/minute.


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