Question
Let , R be such that the function f(x)= cases 2 (x^ 2 -2 )+2 x &, x be differentiable at all x R . Then 34( + ) is equal to
JEE Main
Mathematics
Continuity and Differentiability
2026
JEE Main 2026 (24 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 36
- B. 24
- C. 84
- D. 48
Answer
D. 48
Step-by-step solution
f(x) = cases 2 x^2 + 2 x - 4 & ; x f(1^-) = 2 - + 3, f(1) = -2 + 2 2 - + 3 = 2 - 2 4 - 3 + 3 = 0 ...(1) f'(1^+) = 4 + 2 , f'(1^-) = + 3 4 + 2 = + 3 3 + 2 - 3 = 0 ...(2) Solving (1) & (2) We get = 3 17 , = 21 17 34( + ) = 34 27 17 = 48
Related: Mathematics — Continuity and Differentiability · All PYQ Banks