NCERT Class 12 · Ch 5 Exercise 5.2 · Q10
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.2 Question 10
Prove f(x)=⌊x⌋, 0<x<3, is not differentiable at x=1,2.
💡 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: Neither derivative exists.
- At either integer n=1 or 2, f(n)=n; the left limit is n−1 while the right limit is n.
- The function is discontinuous at both points. Differentiability implies continuity, so it is not differentiable there.
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