Hi community,
"Could you please explain to me how the method FB_init works? The block inside it states, 'the retain variables are initialized (reset warm / reset cold).' Every time I perform a 'cold' reset on the PLC, do I need to call FB_init? Am I thinking correctly?"
Then I do that

VAR_GLOBAL PERSISTENT
x: UINT;
END_VAR

Create function block

{attribute 'call_after_init'}
FUNCTION_BLOCK Test
VAR_INPUT
    y:                          INT;
END_VAR
VAR 
    output                      :INT;
END_VAR
output:=y*y;

Create FB_init of function block

METHOD FB_init : BOOL
VAR_INPUT
    bInitRetains : BOOL; // if TRUE, the retain variables are initialized (warm start / cold start)
    bInCopyCode : BOOL;  // if TRUE, the instance afterwards gets moved into the copy code (online change)
END_VAR
gvl.x:=gvl.x+1;

Create main program

PROGRAM MAIN
VAR
    test: test;
END_VAR
test(y:=15);
test(y:=16);

I'm currently performing a cold reset on the PLC, and the value of 'x' is supposed to increase. However, the value of 'x' remains unchanged at 1 all the time. The variable 'x' is of the PERSISTENT type so a cold reset of the PLC doesn't to have any impact on it.
Why can explain for me why that happen?

Your anwsers are here: https://content.helpme-codesys.com/en/CODESYS%20Development%20System/_cds_method_fb_init_fb_reinit.html

You are trying to make something very simple really complex, but my best guess is that the order of execution is:
- initialize FB (x becomes 1)
- Load persistent (x is 1)
- start application (x remains 1)

PS, It could also be that your "persistent" variables are not stored correctly and that, at startup, the value is always 0. Did you add this variable to the Persistent Variable list? And did you make sure that this works correctly on the device you are using?
So maybe the execution order is:
- load persistent (x is 0, because it was not stored correctly)
- initialize FB (x becomes 1)
- start application (x remains 1)