Question

What is the formula for Lagrange’s theorem?

(a) f’(c) = \(\frac {f(a)+f(b)}{b-a}\)

(b) f’(c) = \(\frac {f(b)-f(a)}{b-a}\)

(c) f’(c) = \(\frac {f(a)+f(b)}{b+a}\)

(d) f’(c) = \(\frac {f(a)-f(b)}{b+a}\)

I have been asked this question during an interview for a job.

Enquiry is from Mean Value Theorem in portion Continuity and Differentiability of Mathematics – Class 12

Answer 1

Right answer is (b) f’(c) = \(\frac {f(b)-f(a)}{b-a}\)

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 the formula for Lagrange’s theorem is f’(c) = \(\frac {f(b)-f(a)}{b-a}\).