Carrots start deteriorating as soon as they're picked, but that's not to say they go bad right away. Carrots actually have a shelf life of around eight months after harvest. There are different stages of deterioration, though, ranging from limpness to a funky odor. For maximum freshness, store carrots in a sealed plastic bag in the refrigerator.
To extend the shelf life of cut carrots to about a week, keep them in a container of ice water in the fridge. Evidence of mild deterioration includes limpness and little white dots known as white blush. These are signs of dehydration and only affect texture and appearance; the carrots are still good to eat, they're just not at the peak of freshness. Fine roots growing from the tips of carrots and sprouting greens on the tops are further signs of deterioration. Again, the carrots aren't spoiled, just past their prime. You might find these carrots have a mildly bitter taste when they reach this stage. You have no doubts about spoilage when you come across a rotten carrot. Black mold, a musty smell, darkened flesh and oozing, mushy flesh all let you know to stay away from these guys. If your carrots show these signs, toss them.