Question

Function f is differentiable on [a,b] to satisfy Lagrange’s mean value theorem.

(a) True

(b) False

This question was addressed to me in my homework.

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

Answer 1

Right choice is (a) True

The explanation: According to Lagrange’s mean value theorem, if f : [a,b] → R is a function such that f is differentiable on (a,b) then there exists a least point c ∈ (a,b) such that f’(c) = \(\frac {f(b)-f(a)}{b-a}\). This shows Function f is differentiable on [a,b].