Let I be a closed interval and f : I → ℝ be a differentiable function. Then the derivative f' of f has the intermediate value property : if a , b ∈ I with a < b , then for every y ∈ ℝ such that f' ( a ) < y < f' ( b ) or f' ( b ) < y < f' ( a ), there exists x ∈ [ a , b ] such that f' ( x ) = y .