A differentiable function f (x) satisfies f (0) = 0 and f(1…

Maths Differentiation and Applications of Derivatives NTA Abhiyas Question - Applications of Derivativas Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

A differentiable function f (x) satisfies f (0) = 0 and f(1) = sin 1, then (where f' represents derivative of f)

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The correct answer is:

f' = cos c for some c [0,1]

Let, g (x) = f (x) - sin a?

Now, g (0) = f (0) - 0 = 0 &g (1) = f(1) - sin 1 = 0

As g (x) is differentiable, so by Rolle's theorem,

g' = 0 for some c [0,1]

i.e. f' - cosc = 0

f ' = cos c for some c [0, 1]

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