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  4. The side of a square sheet is increasing at the rate of 4 cm per minute. The rate by which the area increasing when the side is 8 cm long is-

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Q. The side of a square sheet is increasing at the rate of $4 \,cm$ per minute. The rate by which the area increasing when the side is $8\, cm$ long is-

Application of Derivatives

Solution:

$A = x ^2, \frac{ dx }{ dt }=4\, cm / \min$
$\frac{ dA }{ dt }=2 x \frac{ dx }{ dt }=8 x$
$\Rightarrow$ at $x=8 \, cm$
$\frac{ dA }{ dt }=64 \, cm ^2 / \min$.