I can't be sure as you don't remember the function, but it is possibly because you didn't find the second derivative of the function. You see, the first derivative can equal zero indicating a local extrema. However, if the second derivative also equals zero at this point it is undefined. The case may be that the function did not have a real value at zero. This is what some call a discontinuity. There may even be a limit as the function approaches zero, but still have no value at that point. Again, the second derivative test would allow you to make this distinction.

Also, if the function had no values for x less than zero, it looks like there would be a relative maximum at zero.