Verify Rolles theorem for the function `f(x)=log{(x^2+a b)/(x(a+b))}` on `[a ,\ b]` , where `0

Explanation

Given `f(x)=\log \{(x^{2}+a b) /(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)`


Also, `f(a)=\log (\frac{a^{2}+a b}{a(a+b)})=\log 1=0`
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