Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Using Rolle's theorem show that the derivative of the function f(x) = 
vanishes at an infinite set of points of the interval (0, 1).
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
f(x) = 0 ⇒ sin 
= 0 ⇒ 
= n π
⇒ x = 
, n ∈ N
x = ......., 
, 
, ......., 
, 
1.
Consider interval 
= 0 = 
By Rolle ’ s theorem f ′ (x) vanishes at least once in 
Infinite number of such intervals are there. Hence f ′ (x) vanishes at infinite number of points in (0, 1)
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