verify rolles theorem for the function f(x) = cos (1/x ) for -1 =x =1 - Maths - Continuity and Differentiability

Question

verify rolles theorem for the function f(x) = cos (1/x ) for
-1<=x<=1

Jegannathan Anandaraman · Accepted Answer

Hello Ashutosh dear, the function has to be f(x) =
cos​-1(1/x) for [-1,+1]
Funtion is continuous for closed interval
It is also differentiable for open interval ​(-1,+1)
But f(-1) ​≠ f(1)
So Rolle's theorem cannot be applied

verify rolles theorem for the function f(x) = cos (1/x ) for -1<=x<=1