MHT CET · Maths · Application of Derivatives
The length and breadth of a rectangle are \(x \mathrm{~cm}\) and y cm respectively. If the length decreases at the rate of \(5 \mathrm{~cm} /\) minute and the breadth increases at the rate of \(3 \mathrm{~cm} /\) minute, then the rates of change of the perimeter and area respectively when the length is 5 cm and breadth is 2 cm , are
- A -4 and 5
- B -5 and 3
- C 3 and 5
- D 3 and -5
Answer & Solution
Correct Answer
(A) -4 and 5
Step-by-step Solution
Detailed explanation
\(P = 2(x+y) \implies \frac{dP}{dt} = 2\left(\frac{dx}{dt} + \frac{dy}{dt}\right)\) \(\frac{dP}{dt} = 2(-5 + 3) = -4 \mathrm{~cm/min}\)
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