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Mathematics · JEE | APPLICATION OF DERIVATIVES
हिन्दीThe length \( x \) of a rectangle is decreasing at the rate of \( 3\text{ cm/minute} \) and the width \( y \) is increasing at the rate of \( 2\text{ cm/minute} \). When \( x = 10\text{ cm} \) and \( y = 6\text{ cm} \), find the rate of change of the area of the rectangle.
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Correct answer · Option A
\( 2\text{ cm}^2/\text{min} \)
Explanation
Area \( A = x \cdot y \implies \frac{dA}{dt} = \frac{dx}{dt}y + x\frac{dy}{dt} = (-3)(6) + (10)(2) = -18 + 20 = 2\text{ cm}^2/\text{min} \).
