Question

Cauchy’s Mean Value Theorem can be reduced to Lagrange’s Mean Value Theorem.

(a) True

(b) False

I got this question during an interview for a job.

Asked question is from Cauchy’s  Mean Value Theorem in division Differential Calculus of Engineering Mathematics

Answer 1

Correct choice is (a) True

To explain I would say: Cauchy’s Mean Value Theorem is the generalized form of Lagrange’s Mean Value Theorem and can be given by,

\(\frac{f'(a+θh)}{g'(a+θh)} = \frac{f(a+h)-f(a)}{g(a+h)-g(a)}, 0 < θ < 1\)

Hence, if g(x) = x, then CMV reduces to LMV.