NCERT Class 12 · Ch 6 Exercise 6.3 · Q15
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 15
Find positive x,y with x+y=35 maximizing x²y⁵.
💡 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: x=10, y=25.
- Use the fixed sum to express the second number in terms of x. The objective is \(x^{2} \left(35 - x\right)^{5}\) on (0,35).
- Differentiate: \(- 7 x \left(x - 35\right)^{4} \left(x - 10\right)\). The feasible interior stationary point is x=10.
- The second derivative there is \(-27343750\). The objective tends to zero at the positive-domain endpoints and has only this interior maximum.
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