Class 12 Continuity And Differentiability · Long Answer3 Markscontinuity_parameters
Class 12 Maths · Continuity And Differentiability · Long Answer #125
For f(x)=x²+3x+a when x≤1 and bx+2 when x>1, find a,b for differentiability at 1.
✅ Step-by-Step Solution
Final Answer: a=3,b=5
- Continuity requires 1+3+a=b+2, hence b=a+2.
- The left slope at 1 is 2·1+3=5; the right slope is b.
- Equality gives b=5, then a=b−2=3. These constants also satisfy continuity.
- Therefore a=3,b=5.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Continuity requires 1+3+a=b+2, hence b=a+2.
- [1 mark] The left slope at 1 is 2·1+3=5; the right slope is b.
- [1 mark] Equality gives b=5, then a=b−2=3. These constants also satisfy continuity.
- [0.5 marks] Therefore a=3,b=5.
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