NCERT Class 12 · Ch 5 Exercise 5.2 · Q9
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.2 Question 9
Prove f(x)=|x−1| is not differentiable at x=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: Left derivative −1; right derivative 1, so no derivative at 1.
- The difference quotient at 1 is |h|/h.
- For h<0 it is −1; for h>0 it is 1. These one-sided limits differ.
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