Question

Does Rolle’s theorem applicable if f(a) is not equal to f(b)?

(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

Answer 1

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