JEE Advanced Mathematics question

MathematicsContinuity and DifferentiabilityJEE Advanced

If for all then

Answer: (A),(B),(C)

Solution

Let , , (constants), so . Then

f'(x) = + 2ax + b, f''(x) = 6x + 2a, f'''(x) = 6.

Hence ; ; . Solving: $3 + a + 12 +

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Question ID VK-109243