If f : [a,b] → ℝ is continuous and y is between f(a) and f(b), then ∃c ∈ [a,b] with f(c) = y. Follows from completeness of ℝ.
If f : [a,b] → ℝ is continuous and y is between f(a) and f(b), then ∃c ∈ [a,b] with f(c) = y. Follows from completeness of ℝ.