CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/3 · Q232 Markscontinuity
CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/3 · Question 23 (Continuity And Differentiability)
Find a,b for continuity of f(x)=2 for x≤3, ax+b for 3<x<5, and 5 for x≥5. OR If \(2y^3+y=2x\), prove \(y^{\prime\prime}=-48y/(6y^2+1)^3\).
Alternative 1 2 Marks
Find a,b for continuity of f(x)=2 for x≤3, ax+b for 3<x<5, and 5 for x≥5.
Answer: a=3/2, b=−5/2.
- Continuity requires 3a+b=2 and 5a+b=5.
- Subtract to get 2a=3, then b=2−9/2.
- Hence a=3/2 and b=−5/2.
Alternative 2 2 Marks
If \(2y^3+y=2x\), prove \(y^{\prime\prime}=-48y/(6y^2+1)^3\).
Answer: y″=−48y/(6y²+1)³.
- Differentiate once: (6y²+1)y′=2.
- Differentiate y′=2/(6y²+1) to obtain y″=−24yy′/(6y²+1)².
- Substitute y′ to get −48y/(6y²+1)³.