Let $f$ be a function of the form
$$ f(x) = - 2\sqrt{\frac{x a_0}{x b_0 + c_0}} + \sum_{n=0}^N \frac{x a_n}{x b_n + c_n},$$
where $a_n$, $b_n$, $c_n > 0$, $N > 0$ is an integer and constant, $x \in [0, x_{\mathrm{max}}]$. Does anyone have a solution or hint to find the extreme points of $f$, i.e., $f_{\max}$, $f_{\min}$?