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Question

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 rates of change of the area of rectangle(in cm2/min).

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Solution

It is given that length (x) is decreasing at the rate of 5 cm/min

and the width (y) is increasing at the rate of 4 cm/min,
dxdt=5 cm/min and dydt=4 cm/min
Thus the area (A) of a rectangle is, A=xy
(dAdt)x=8,y=6=(ydxdt+xdydt)x=8,y=6=6(5)+8(4)=2 cm2/min
Hence, the area is increasing at the rate of 2 cm2/min.

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