Bobbi Kristina One Positive Sign ... But Still in Peril

2/2/2015 8:15 AM PST

Doctors saw a slight glimmer of hope for Bobbi Kristina Monday morning -- but they remain clear she's not out of the woods. 

Sources connected to the Houston family tell TMZ ... doctors were testing BK's brain reaction to different stimuli, and saw "minimal response" during one of the tests. We're told doctors view this as a very slight improvement -- but it's enough to delay any immediate discussion of turning off life support.

As we've reported ... the situation has been bleak, and we're told just last night the family started discussing funeral arrangements.

Bobbi Kristina's been in a medically induced coma since Saturday ... when she was found unconscious in her bathtub.