Question

Another form of Rolle’s theorem for the continuous condition is _____

(a) f is continuous on [a,a-h]

(b) f is continuous on [a,h]

(c) f is continuous on [a,a+h]

(d) f is continuous on [a,ah]

The question was asked at a job interview.

I want to ask this question from Mean Value Theorem in division Continuity and Differentiability of Mathematics – Class 12

Answer 1

Correct option is (c) f is continuous on [a,a+h]

The best I can explain: According to Rolle’s theorem, if f : [a,a+h] → R is a function such that

i) f is continuous on [a,a+h]

ii) f is differentiable on (a,a+h)

iii) f(a) = f(a+h) then there exists at least one θ c ∈ (0,1) such that f’(a+θh) = 0