In which states should I linearize the system? $\dot{x} =f(x,u)$

Question

Let's say that I have a nonlinear ODE-system on first order:

$$\dot{x} =f(x,u)$$

And I know when the system is static

$$0 = f(x_e, u_e)$$

But in what states should I linearize the system? Because the state vector $x_e$ contains position and zero velocity.

Question:

In which states should I linearize the system? Can I linearize the system so the second order system becomes zero, e.g zero acceleration?

$$\ddot{x} = F(x, u)$$ $$0 = F(x_e, u_e)$$

Or in what states $x$ and input $u$ should I linearize in?