This is my lecturer's Darboux Theorem, however I have a problem with one of the steps there, I signed it wih ***. He said xmin is not equal to a and b. Buf if it is equal then what? I mean intuitively when I think about it if it is equal then I cant get c such that f ' (c)=0 but still can I just say xmin is not equal to a and b? Isn't that specific case? Thank you.