Mean value theorem of a function in [a,b] Is Mean Value Theorem (Rolle's Theorem) applicable for the following function:

$$\log \frac{x^2 + ab}{(a+b)x}$$

in the interval $(a,b)$

My text says that it's applicable. But isn't the function discontinuous when $a&lt;0$ and $b&gt;0$? As this interval include $0$ at which the function is not defined and hence is not continuous.
yes this function fulfills the conditions of Rolle's theorem.
$f(x)$ is continous at the interval $[a,b]$ as a composition of continously functions and is differentiable. Also we can prove that $f(a)=f(b)=0$.
Sonnhard.
yes this function fulfills the conditions of Rolle's theorem.
$f(x)$ is continous at the interval $[a,b]$ as a composition of continously functions and is differentiable. Also we can prove that $f(a)=f(b)=0$.
Sonnhard.