Question

Rolle’s Theorem tells about the

(a) Existence of point c where derivative of a function becomes zero

(b) Existence of point c where derivative of a function is positive

(c) Existence of point c where derivative of a function is negative

(d) Existence of point c where derivative of a function is either positive or negative

I have been asked this question in an internship interview.

I want to ask this question from Rolle’s Theorem in section Differential Calculus of Engineering Mathematics

Answer 1

Correct option is (a) Existence of point c where derivative of a function becomes zero

Explanation: Statement of Rolle’s Theorem is that, If function f(x) attains same value at point ‘a’ and ‘b’ [f(a) = f(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) and f’(c) = 0.