The server generates a function *f* (x) of one real variable x, containing
parameters a_{1},a_{2},..., which 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* (x) 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.

Choose the level of difficulty suitable for you: 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 .

There is also a
detailed menu for the parameters of this exercise.
The most recent version

Please take note that WIMS pages are interactively generated; they are not ordinary HTML files. They must be used interactively ONLINE. It is useless for you to gather them through a robot program.

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, derivability, limit