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NCERT Class 12 · Ch 6 Exercise 6.1 · Q7

NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.1 Question 7

A rectangle length x decreases at 5 cm/min and width y increases at 4 cm/min. At x=8 cm,y=6 cm find (a) perimeter and (b) area rates.

Instantaneous rectangle: 8 cm × 6 cm

💡 Concept Hints

Identify the domain and the inner and outer functions, or the relevant one-sided limits.
Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.

✅ Step-by-Step Solution

Final Answer: (a) −2 cm/min; (b) 2 cm²/min.

Use signed rates xₜ=−5, yₜ=4. P=2(x+y) gives Pₜ=2(−5+4)=−2 cm/min.
A=xy gives Aₜ=yxₜ+xyₜ=6(−5)+8(4)=2 cm²/min.

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All Questions in Applications Of Derivatives — Exercise 6.1

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