Linearizing \dot{x}+√x = 0 when the derivative is undefined at equilibrium

[FaroukSchw]

Hello ,
I am trying to linearize $\dot{x}$+√x = 0. The only equilibrium point is at x=0; but the derivative is not defined at this point. Does anybody have a suggestion?
Regards.

 

[Office_Shredder]

Why are you trying to linearize it?

 

[FaroukSchw]

hello Office_Shredder
I just got interested in it when talking to a friend about problems that we can encounter

 

[HallsofIvy]

$\sqrt{x}$ cannot be linearized at x= 0 precisely because its derivative does not exist.