Q. 22

Discuss the applicability for Rolle’s theorem, when:

, where

Answer :

Condition (1):


Since, f(x)=(x-1)(2x-3) is a polynomial and we know every polynomial function is continuous for all xϵR.


f(x)= (x-1)(2x-3) is continuous on [1,3].


Condition (2):


Here, f’(x)= (2x-3)+ 2(x-1) which exist in [1,3].


So, f(x)= (x-1)(2x-3) is differentiable on (1,3).


Condition (3):


Here, f(1)= (1-1)(2(1)-3)=0


And f(5)= (3-1)(2(3)-3)=6


i.e. f(1)≠f(3)


Condition (3) of Rolle’s theorem is not satisfied.


So, Rolle’s theorem is not applicable.


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