1. The problem statement, all variables and given/known data Okay I know my title sucks but if you have a better one let me know, here is the question: If I have a continuous function on a closed interval [a,b] and let N be any number between f(a) and f(b), where f(a) is not equal to f(b), then which theorem guarentees that there must be some input c between a and b such that f(c) equals N? 3. The attempt at a solution Here is what I was thinking the Professor means, interval [a,b] is just the domain including a and b, N is maybe difference in y value between a function at a vs b? Is c a value of x for the function and he wants to know where it is equal to this difference? Admittedly I am lost to what is this thing is saying, can someone translate it?