EDB — 1D9

Exercises

1. [1D9]Let $f:ℝ\to ℝ$ be continuous and differentiable, and $a,b\in ℝ$ with $a<b$. Show that, if $f^{\prime }(a)=f^{\prime }(b)$, then $𝜉$ exists with $a<𝜉<b$ such that

   $$f^{\prime }(𝜉)=\frac{f(𝜉)-f(a)}{𝜉-a}.$$