EDB — 1DW

Exercises

1. [1DW]Difficulty:*.Let \(f_ 0,f_ 1:ℝ→ℝ\), \(f_ 0,f_ 1∈ C^∞\) with \(f'_ 0,f'_ 1{\gt}0\) and \(f_ 1(1){\gt}f_ 0(0)\): then one can interpolate with a function \(f∈ C^∞\) that satisfies

   \begin{eqnarray*} f(x) = f_ 0(x)~ ~ \text{if}~ ~ ~ x≤ 0 \\ f(x) = f_ 1(x)~ ~ \text{if}~ ~ ~ x≥ 1 \end{eqnarray*}

   so that the interpolant has \(f'{\gt}0\).

   What if \(f_ 1(1)=f_ 0(0)\)?

   Solution 1

   [1DX]↺↻