1. The problem statement, all variables and given/known data Suppose f: (a,b)→R where (a,b)[itex]\subset[/itex]R is an open interval and f is a differentiable function. Assume that f'(x)≠0 for all x[itex]\in[/itex](a,b). Show that there is an open interval (c,d)[itex]\subset[/itex]R such that f[(a,b)]=(c,d), i.e. f is surjective on (c,d). 2. Relevant equations f is surjective if for all y[itex]\in[/itex]R there exists an x[itex]\in[/itex]X such that f(x)=y. 3. The attempt at a solution I think I'm supposed to use ε and δ for this proof but I'm not sure where to start. Any clues would be great! Thanks.