homework and exercises - Why are the Lagrangian points $L_1$, $L_2$ & $L_3$ unstable?

Why are the Lagrangian points $L_1$, $L_2$ & $L_3$ unstable? I am doing a physics presentation in front of my class and I am just confirming this is correct, and if it isn't, could somebody provide an explanation.

$F=mv^2/r$ and $v=2\pi/T$

Therefore:

$F=4\pi^2mr/T^2$

$F\propto 1/T^2$ while $r$ is constant.

So if $r$ stops being in the same point as the Lagrange point, then the period of orbit will change and the system will fall out of place.