At what point should carrots be thrown away?
We tend to buy a big bag of carrots from the supermarket (mainly because it's cheaper than a small bag), but usually these are starting to go soft halfway through the week. My current rule of thumb is that I'll cook them until they are so soft that I just can't peel them, and won't eat them raw after they have started to go soft.
Given that this is entirely based on my guesswork, can anyone tell me at what point they are actually inedible?
I cannot answer the at which point are they inedible, but this link addresses the storage question.
Related Q: How to properly store carrots http://cooking.stackexchange.com/q/15517/6808
I edited out the second part of your question because it's a duplicate of the link I posted above. This way, answers here can focus on your main question - how to tell if carrots have become inedible.
If your carrots are going soft after just a few days, you're not storing them properly. Mine keep for weeks and weeks. I leave them in the plastic bag, and keep that in one of the vegetable drawers in my fridge. How are you storing yours?
A rubbery soft carrot isn't bad for you, it just isn't very pleasant. A slimy carrot is bad for you, don't eat it.
And you can typically resuscitate softening carrots by wrapping them in damp paper towels and allowing them to rehydrate.
I'd like to add that when you store them in the plastic-bag in the fridge, make sure you do NOT have water collecting at the bottom of the bag. I usually put a paper-towel in what ends up being the bottom, because sometimes (not always.. depends a lot on the weather naturally!) I end up having some condensed water in the plastic-packaging.