Question

Function f is not continuous on [a,b] to satisfy Lagrange’s mean value theorem.

(a) False

(b) True

I got this question in an online interview.

I'm obligated to ask this question of Mean Value Theorem in section Continuity and Differentiability of Mathematics – Class 12

Answer 1

The correct choice is (a) False

The explanation: According to Lagrange’s mean value 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) then there exists a least point c ∈ (a,b) such that f’(c) = \(\frac {f(b)-f(a)}{b-a}\).