If f(x) = ax² + bx for x ≤ 1 and f(x) = cx + d for x > 1 is differentiable at x = 1, then:

If f(x) = ax² + bx for x ≤ 1 and f(x) = cx + d for x > 1 is differentiable at x = 1, then:

• A. a + b = c + d
• B. 2a + b = c
• C. Both a + b = c + d and 2a + b = c
• D. a = c and b = d

Answer: C) Both a + b = c + d and 2a + b = c

Explanation: For continuity, LHL = RHL at x = 1 → a + b = c + d. For differentiability, LHD = RHD at x = 1. LHD = 2ax + b → 2a + b. RHD = c. Thus, 2a + b = c.