Question

What are/is the conditions to satify Lagrange’s mean value theorem?

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

(b) f is differentiable on (a,b)

(c) f is differentiable and continuous on (a,b)

(d) f is differentiable and non-continuous on (a,b)

I have been asked this question in an online interview.

Origin of the question is Mean Value Theorem in division Continuity and Differentiability of Mathematics – Class 12

Answer 1

Right choice is (c) f is differentiable and continuous on (a,b)

For 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) = \(\frac {f(b)-f(a)}{b-a}\).