NCERT Class 12 · Ch 6 Exercise 6.2 · Q15
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 15
If interval I is disjoint from [−1,1], prove f(x)=x+1/x is increasing on I.
💡 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: Strictly increasing on I.
- Every x∈I satisfies |x|>1. The interval lies wholly in one of the two domain components.
- f′=1−1/x²=(x²−1)/x²>0 there. Apply the derivative criterion on I.
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