Question

Mean Value theorem is applicable to the

(a) Functions differentiable in closed interval [a, b] and continuous in open interval (a, 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)

(d) Functions differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’

This question was posed to me in examination.

My question comes from Lagrange’s Mean Value 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)

The explanation: Statement of Mean Value Theorem is that, If function f(x) is 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) = [f(b)-f(a)]/(b-a).