NCERT Class 12 · Ch 6 Exercise 6.3 · Q28
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 28
Find the minimum over real x of (1−x+x²)/(1+x+x²).
💡 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: D: 1/3, at x=1.
- The denominator x²+x+1=(x+1/2)²+3/4 is positive.
- Subtract 1/3: (x²−x+1)/(x²+x+1)−1/3=2(x−1)²/[3(x²+x+1)]≥0. Equality holds at x=1.
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