The derivative of $f(x)=\frac{1}{x}$ is always negative for all $x$ except $x=0$ (where it is not defined). But $f(-1)<f(1)$ , so the statement that $f(x)$ either decreases or remains constant as $x$ increases for all $x$ does not seem to be holding good here. So , can I say that $f(x)=\frac{1}{x}$ a monotonic-decreasing function?

Thanks !