NCERT Class 12 · Ch 6 Exercise 6.3 · Q16
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 16
Find positive numbers with sum 16 and minimum sum of cubes.
💡 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 and 8; minimum cube sum 1024.
- Use the fixed sum to express the second number in terms of x. The objective is \(x^{3} + \left(16 - x\right)^{3}\) on (0,16).
- Differentiate: \(96 \left(x - 8\right)\). The feasible interior stationary point is x=8.
- The second derivative there is \(96\). Completing the square or the derivative sign change confirms the global extremum.
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