EDB — 1F4

Exercises

1. [1F4]Prerequisites:[1F1]↺↻.Difficulty:*.Let \(f:ℝ→[0,∞)\) be a function of class \(C^∞\) such that \(f(0)=0\), \(f(x){\gt}0\) for \(x≠ 0\), and \(f''(0)≠ 0\): show that

   \[ g(x)= \begin{cases} \sqrt{f(x)} & se ~ x≥ 0\\ -\sqrt{f(x)} & se ~ x{\lt} 0 \end{cases} \]

   is of class \(C^∞\).

   Solution 1

   [1F5]↺↻