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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 the rectangle.
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Solution
A = xy ....(i)
Differentiating (i) w.r.t.t, we get,
`(dA)/dt = x dy/dt + y dx/dt`
= (8 cm) (4 cm/min) + (6 cm) (-5 cm/min)
= 2 cm2 /min
∴ Area of the rectangle is increasing at a rate of 2 cm2/min
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