How to show that $f(x)=1/x^2$ is uniformly continuous on $x\ge1$? For my homework I have to show that $f(x)=1/x^2$ is uniformly continuous on the interval $[1,∞)$, and I have absolutely no idea what to do. 
Please don't give me the answer, but if you could push me in the right direction, I would really appreciate it. 

Since $f'(x)=-\frac{2}{x^3}$ is bounded on $I=[1,+\infty)$, $\left|f'(x)\right|\leq 2$ gives that $f(x)$ is Lipschitz-continuous on $I$, hence uniformly continuous. 
