NCERT Class 12 · Ch 6 Exercise 6.1 · Q13
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.1 Question 13
A spherical balloon diameter is (3/2)(2x+1). Find dV/dx.
💡 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: (27π/8)(2x+1)², for x>−1/2.
- Radius is half the diameter: r=(3/4)(2x+1). A positive radius requires x>−1/2.
- V=(4π/3)r³=(9π/16)(2x+1)³. Differentiate to get (27π/8)(2x+1)².
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