Question

Cauchy’s Mean Value Theorem is also known as ‘Extended Mean Value Theorem’.

(a) False

(b) True

This question was posed to me in a national level competition.

I'm obligated to ask this question of Cauchy’s  Mean Value Theorem in portion Differential Calculus of Engineering Mathematics

Answer 1

Right answer is (b) True

The best I can explain: Mean Value Theorem is given by, \(\frac{f(b)-f(a)}{b-a} = f'(c),\) where c Є (a, b).

This theorem can be generalized to Cauchy’s Mean Value Theorem and hence CMV is also known as ‘Extended’ or ‘Second Mean Value Theorem’.