Let f(x) = g ′ (x) , where g ′ is the derivative of g and …

Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let f(x) = g ′ (x) , where g ′ is the derivative of g and is a continuous function then f(x) exist if

g(x) is polynomial

g(x) = x

g(x) = x 2

g(x) = x 3 h(x) where h(x) is a polynomial

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(c, d)

= = 1

and = = –1

Hence f(x) exists if g ′ (0) = 0

If g(x) = ax + b, a ≠ 0 then f(x) = a and f(x) = –a.

Hence f(x) exists if g(x) = x 2 or g(x) = x 3 h(x) where h(x) is a polynomial.

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