This is probably not the best comparison but....here it goes anyway.
My neighbor has a very aggressive half pit mutt. It has gotten out on a few occasions. My garbage pails are on the side of the house, as I was taking trash out this thing got loose. Usually it barks, growls and bares it teeth, on this occasion my back was turned and I had no idea it was there. I happened to have my spyderco endura opened still in my hand because I was cutting cardboard. I heard the movement in the brush and turned immediately to see it charging at me. I put that tip of the endura right out there and readied for that pit. That dog got about half a foot from the tip of that blade dead stopped in it's tracks and literally walked backwards through the brush growling low baring its teeth and watching me the whole time. I have never seen anything like that before ( I work outdoors so it's not the first time I have had to go toe to toe with nature ). I still don't know whether it was the knife or my posture because at the time I full on thought I was going to have to end that dogs existence.
Probably not the best example but I do think every living thing has a tendency towards self preservation, I don't think too many things would dive head first into a sharp pointed object a second time.
However if it was me a .357 mag at the VERY LEAST. Prepare for the worst, hope for the best. ex. what if it's the bear and not the mountain lion!