EDB — 1CV

Exercises

1. [1CV]Let \(I=(a,b)⊂ℝ\) be an open interval. Let \(f:I→ℝ\) be differentiable: show that \(f'\) is continuous, if and only if for every \(x\)

   \[ f'(x) = \lim _{(s,t)→ (x,x), s≠ t} \frac{f(t)-f(s)}{t-s} ~ . \]
   Solution 1

   [1CW]↺↻