NCERT Class 12 · Ch 6 Exercise 6.1 · Q2
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.1 Question 2
A cube volume increases at 8 cm³/s. Find the surface-area rate when its edge is 12 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: 8/3 cm²/s.
- Let the edge be u. V=u³ and A=6u²; hence Vₜ=3u²uₜ and Aₜ=12uuₜ.
- At u=12, uₜ=8/(3·144)=1/54 cm/s, so Aₜ=12·12/54=8/3 cm²/s.
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