NCERT Class 12 · Ch 6 Exercise 6.3 · Q14
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 14
Find positive x,y with x+y=60 maximizing xy³.
💡 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=15, y=45.
- Use the fixed sum to express the second number in terms of x. The objective is \(x \left(60 - x\right)^{3}\) on (0,60).
- Differentiate: \(- 4 \left(x - 60\right)^{2} \left(x - 15\right)\). The feasible interior stationary point is x=15.
- The second derivative there is \(-8100\). The objective tends to zero at the positive-domain endpoints and has only this interior maximum.
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