You have a number of issues. This does not do as you expect:
num is a pointer to the array. Sizeof num is merely the size of a pointer, not the size of the array. If you get MAX entries, pass MAX as the size. You need to make sure you get MAX entries, though. Input can fail. Suppose the user enters 'A' instead of a number. You're screwed without ever being kissed. Always check your input functions for success.
See scanf and its return value for details.
Once you get into the "smallest" function, set up a loop that runs from 0 to size-1. Put the first value into a variable. Compare each following value to the variable. If it's smaller, put it in the variable. If not, just go on to the next. When you're through, return the variable.