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Class 12 Continuity And Differentiability · Short Answer2 Marksdifferentiability

Class 12 Maths · Continuity And Differentiability · Short Answer #48

Let f(x)=ax+b for 0<x≤1 and f(x)=2x²−x for 1<x<2. Find a,b so that f is differentiable on (0,2).

✅ Step-by-Step Solution

Final Answer: a=3,b=−2
  1. Only x=1 is a junction. Continuity requires a+b=2−1=1.
  2. The branch slopes at 1 are a and 4·1−1=3. Equality gives a=3, then b=1−3=−2.
  3. Thus a=3,b=−2 make f differentiable throughout (0,2).

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Only x=1 is a junction. Continuity requires a+b=2−1=1.
  • [1 mark] The branch slopes at 1 are a and 4·1−1=3. Equality gives a=3, then b=1−3=−2.
  • [0.5 marks] Thus a=3,b=−2 make f differentiable throughout (0,2).

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