The server generates a function $f$ of one real variable, containing parameters ${a}_{1}$, ${a}_{2}$,..., hich is defined by different formulas on two segments of an interval. Your aim is to find values for these parameters ${a}_{i}$ such that $f$ is continuous and differentiable to a required order.

One can solve the problem either by a Taylor expansion, or by successive derivations. In the difficult cases, the resolution of a system of linear equations is also necessary.

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Description: parametrize a function to make it differentiable to a required order. interactive exercises, online calculators and plotters, mathematical recreation and games

Keywords: interactive mathematics, interactive math, server side interactivity, analysis, algebra, continuity, derivative, limit