I want to find the points of discontinuity of the following function:
$$f(x)=\log\left|{\frac{x+2}{x+3}}\right|$$
This is defined for $x\neq-2$ and $x\neq-3$. I proceed to find the first derivative:
$$f'(x)=\frac{1}{x^2+5x+6}$$
This is as well defined for $x\neq-2$ and $x\neq-3$. Since $f(x)$ is not defined for these points either, they should not be critical points. Therefore there should be no critical points. However, my textbook says "$x=-2$, $x=-3$ are points of discontinuity for $f$". Any hints on what I'm doing wrong?
I think I understand it now. A point of discontinuity is when the function is not continous at that point. It is not necessary to derive the function to determine the point of discontinuity. Simply find the domain and the points of discontinuity will be the extremes of the domain. Instead, a critical point refers to minimums and maximums (the function should be derived).