Q. 1 A4.7( 3 Votes )

Discuss the applicability of Rolle’s theorem for the following functions on the indicated intervals :

f(x) = 3 + (x – 2)2/3 on [1, 3]

Answer :

First, let us write the conditions for the applicability of Rolle’s theorem:


For a Real valued function ‘f’:


a) The function ‘f’ needs to be continuous in the closed interval [a,b].


b) The function ‘f’ needs differentiable on the open interval (a,b).


c) f(a) = f(b)


Then there exists at least one c in the open interval (a,b) such that f’(c) = 0.


(i) Given function is:


on [1,3]


Let us check the differentiability of the function f(x).


Let’s find the derivative of f(x),







Let’s the differentiability at the value of x = 2






f is not differentiable at x = 2, so it is not differentiable in the closed interval (1,3).


So, Rolle’s theorem is not applicable for the function f on the interval [1,3].


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