If the function f(x) = cases 1 |x| , & |x| 2 ax^2 + 2b, & |x| < 2 cases is differentiable on ℝ, then 48(a + b) is equal to ________.

JEE Main 2024 Mathematics question

If the function is differentiable on ℝ, then 48(a + b) is equal to .

Answer: 15

For continuity at x = ±2: 1/2 = 4a + 2b. For differentiability at x = 2: 4a = −1/4, so a = −1/16; at x = −2 the

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Question ID VK-017101