IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 27

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Continuity and Differentiability, with the answer and a step-by-step solution.

Continuity and DifferentiabilityCalculusMultiple choiceMedium

The function

is differentiable at x = 1. Find (a, b).

  1. A

    \left( 2, -1 \right)

  2. B

    \left( 0, 1 \right)

  3. C

    \left( 2, 1 \right)

  4. D

    \left( 1, 0 \right)

Pick an option, then check.
Answer & solution

Answer: Option A

Differentiability at x = 1 requires both continuity and matching one-sided derivatives there.

Continuity: the left-hand value is a(1) + b = a + b and the right-hand value is 1² = 1, so a + b = 1.

Derivatives: the left-hand derivative of ax + b is a, and the right-hand derivative of x² is 2x, which is 2 at x = 1.

So a = 2.

Substituting into a + b = 1 gives b = −1.

Therefore (a, b) = (2, −1).

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