Question

Discuss the applicability of Rolle's thim to the function
F(x)= log [ x² + ab/x (a+b) ] in [a,b] a,b>0.​

Answer 1

Answer:

Given f(x) = log {(x2 + ab)/(x(a + b))} As we know that every logarithmic function is continuous and differentiable in Positive real numbers So it is continuous in [a, b] and differentiable in (a, b) Thus, all the conditions of Rolle’s theorem are satisfied. Now we have to show that there exist a point c in (a, b) such that f'(c) = 0 Hence, Rolle’s theorem is verified.Read more on Sarthaks.com - https://www.sarthaks.com/537357/verify-rolles-theorem-for-the-function-f-x-log-x-2-ab-x-a-b-on-a-b-where-0-a-b