Does Rolle’s theorem applicable if fA. is not equal to fB.?

A. Yes

B. No

C. Under particular conditions

D. May be

The question was asked at a job interview.

This question is from Mean Value Theorem in section Continuity and Differentiability of Mathematics – Class 12

Correct answer is B. No

Easy explanation: According to Rolle’s theorem, if f : [a,b] → R is a function such that

i) f is continuous on [a,b]

ii) f is differentiable on (a,b)

iii) fA. = fB. then there exists at least one point c ∈ (a,b) such that f’C. = 0