<s>[INST] I am trying to find the critical points of the function
$$f(x) = \frac{x^2 - 4x - 5}{x^3 + 4x^2 + 4x}.$$
This function is obviously undefined when the denominator is zero; however, I fail to see how to proceed in actually finding the critical points. What is the best course of action?[/INST]