For what triplets of real numbers (a, b, c) with a ≠ 0 the …

Maths Functions, Limits, Continuity and Differentiability Derivability at a Point and in an Interval Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

For what triplets of real numbers (a, b, c) with a ≠ 0 the function

f(x) = is differentiable for all real x?

{(a, 1 − 2a, a) ⎜ a ∈ R, a ≠ 0 }

{(a, 1 − 2a, c) ⎜ a, c ∈ R, a ≠ 0 }

{(a, b, c) ⎜ a, b, c ∈ R, a + b + c = 1 }

{(a, 1 − 2a, 0) ⎜ a ∈ R, a ≠ 0}

Text Solution

Verified by Experts

The correct answer is:

f(x) =

f(x) should be continous at x =1

it gives a+b+c =1

f(x) should be differentiable at x= 1

it gives 2a+b=1 ⇒ b =1–2a c= 1–a–b= a

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