Numerical analysis

Graphical analysis

DPS.exe analysis

Fixed point

−1.0 (have to solve $f\left(x\right)=x$ for x).

−1.0 (additional programming required).

−1.0 (system generated automatically).

Nature of Fixed point

Repelling (determined from assumption).

Repelling (it is revealed by taking an initial seed near the fixed point and using a graphical cobweb).

Repelling (the system determines this and automatically represents its nature to the user).

Orbit for initial seed x₀ = −1.1

$-1.1\to -1.4\to -1.8\to \cdots$ difficult to continue this process.

Values inserted in the list variable can show using the programming, but a little bit complicated.

The system automatically generates the orbit of $f\left(x\right)$ for a given initial seed inserted by the user. Furthermore, the result is the same as the numerical process.

The fate of orbit for initial seed x₀ = −1.1

A sufficient number of iterations is essential.

As the cobweb is heading towards the significant negative, assume that fate is −∞.

DPS.exe automatically calculates itself and generates the result as −∞.