NCERT Class 12 · Ch 6 Exercise 6.2 · Q11
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 11
Prove f(x)=x²−x+1 is neither strictly increasing nor decreasing on (−1,1).
💡 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: Decreases up to 1/2, then increases.
- f′=2x−1 is negative on (−1,1/2) and positive on (1/2,1).
- Both signs occur inside the specified interval, so the function has neither monotonic behaviour throughout it.
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