Class 12 Continuity And Differentiability · Long Answer3 Marksdifferentiability
Class 12 Maths · Continuity And Differentiability · Long Answer #123
Let f(x)=2x−1 for x<1/2 and f(x)=3−6x for x≥1/2. Discuss differentiability at 1/2.
✅ Step-by-Step Solution
Final Answer: Continuous but not differentiable at 1/2.
- The value at 1/2 is 3−6·(1/2)=0.
- The left and right limits are 2·(1/2)−1=0 and 3−6·(1/2)=0, so f is continuous.
- The left derivative is 2 and the right derivative is −6. They are unequal.
- Therefore f is not differentiable at 1/2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The value at 1/2 is 3−6·(1/2)=0.
- [1 mark] The left and right limits are 2·(1/2)−1=0 and 3−6·(1/2)=0, so f is continuous.
- [1 mark] The left derivative is 2 and the right derivative is −6. They are unequal.
- [0.5 marks] Therefore f is not differentiable at 1/2.
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