Question

Rolle’s theorem is applicable to the

(a) Functions differentiable in closed interval [a, b] and continuous in open interval (a, b) only and having same value at point ‘a’ and ‘b’

(b) Functions continuous in closed interval [a, b] only and having same value at point ‘a’ and ‘b’

(c) Functions continuous in closed interval [a, b] and differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’

(d) Monotonically Increasing funtions

The question was asked during an interview.

The question is from Rolle’s Theorem topic in portion Differential Calculus of Engineering Mathematics

Answer 1

Correct choice is (c) Functions continuous in closed interval [a, b] and differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’

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.