Question

Log[(x^2+ab)/x(a+b)] in[a,b]

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) FIRST PHOTO COMES HERE

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

SECOND PHOTO COMES HERE