EDB — 1C6

[1C6] Let \(I⊆ ℝ\) be an open interval. Let \(f:I→ℝ\) be differentiable, and \(x,y∈ I\) with \(x{\lt}y\). Show that if \(f'(x)⋅ f'(y){\lt}0\) then \(𝜉∈ I\) exists with \(x{\lt}𝜉{\lt}y\) such that \(f'(𝜉)=0\).