Question

If f(a) is euquals to f(b) in Mean Value Theorem, then it becomes

(a) Lebniz Theorem

(b) Rolle’s Theorem

(c) Taylor Series of a function

(d) Leibnit’x Theorem

The question was posed to me in my homework.

The question is from Lagrange’s Mean Value Theorem in section Differential Calculus of Engineering Mathematics

Answer 1

Correct option is (b) Rolle’s Theorem

Explanation: According to Mean Value Theorem, If a function exist at pt. ‘a’, ‘b’ and continuous in closed interval [a, b] and differentiable in open interval (a, b) then there exists a point ‘c’, such that c∈(a, b), Where,

f’(c)= [f(b)-f(a)]/(b-a).

Hence, By putting f(b) = f(a) in the statement of Mean Value Theorem, we get

f’(c) = [f(b)-f(a)]/(b-a) = 0. Which is a statement of Rolle’s Theorem.