Finding cube root of a number less than 1 using binary search
I think I know the problem you're talking about. The only reason she put that is that she deals with the absolute difference: 
while abs(guess**3 - cube) >= epsilon
However, the code will need another line to deal with negative cubes all together which will be something along the lines of:
if cube<0: guess = -guess 
I hope this helps.
I am doing MIT6.00.1x course on edX and the professor tells that "If x<1, search space is 0 to x but cube root is greater than x and less than 1".
There are two cases :

 1. The number x is between 0 and 1

2. The number x is less than 0 (negative)

In both the cases, the cube root of x will lie between x and 1. I understood that. But what about the search space? Will the initial search space lie between 0 and x? I think it is not that. I think the bold text as cited from the lecture is a flaw! Please enlighten me on this.