Does a constant function violate the extreme value theorem? Why/why not?

I feel like I’d be doing your homework for you if I answered this.

The extreme value thm says that a continuous function on [a,b] will have a max and min in that range. Think about the definition of max and min, in regards to a constant function.

The answer to your question depends on how you define those two terms. If you say the max can equal the min, then you’ll have one answer; if you say they have to be unique, you’ll have the other answer.

ok thanks