Question

Verify Rolle’* theorem for the function f(x) = log {(x2 + ab)/(x(a + b))} on [a, b], where 0 < a < b.

Answer 1

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’* theorem are satisfied.

Now we have to show that there exist a point c in (a, b) such that f'(c) = 0

Hence, Rolle’* theorem is verified.