EDB — 1D9

Exercises

1. [1D9]Let \(f:ℝ→ℝ\) be continuous and differentiable, and \(a,b∈ℝ\) with \(a{\lt}b\). Show that, if \(f'(a)=f'(b)\), then \(𝜉\) exists with \(a{\lt}𝜉{\lt}b\) such that

   \[ f'(𝜉)=\frac{f(𝜉)-f(a)}{𝜉-a} ~ ~ . \]