EDB — 1DR

Exercises

1. [1DR] Let it be given \(N\) positive integer. Find an example of a function \(C^∞\) with \(𝜑(x)=0\) for \(x{\lt}0\) while \(𝜑^{(n)}(x){\gt}0\) for \(0≤ n≤ N\) and \(x{\gt}0\).

   Solution 1

   [1DS]↺↻

   Note however that it cannot be required that all derivatives be positive, because of exercise [1N7]↺↻.