In the Algebra tab menu click **Create function**, and choose **domain + formula**. Note that in the entry box, checking existence is now proposed as a default. Enter the formula (*x*+1)/(3*x*‑2).

Figure 36 - Create function by formula + domain

If you keep _{} as the domain of definition, Casyopée will say after validating the function: “This can lead to errors in the plots or calculations; confirm?”. Edit the domain into _{} and click _{}. Casyopée creates a « value of *x* » x1 here equal to 2/3 and rewrites the domain.

If you created this value before, the **Auto** button enters the appropriate domain automatically.

After clicking the |
Figure 37 - List of values of x and mini-diagram |

**Limits**

One can obtain values or limits taken by the selected function for the values existing in the *x-values list*.

Press the function and value at the bottom of the *graphic tab*.

Figure 40 - Symbolic values list

### Derivative

We differentiate our function.

Figure 41 - Menu Calculate / derivative

Select by clicking the expression, it appears highlighted. The **Calculate** button appears. Click this button and choose **derivative**. A *dialogue box* asks for confirmation. Select **Yes**.

Figure 42 - Confirmation box for a derivative

Casyopée opens a dialog box offering to confirm or change the domain. It is because the derivative is not always defined on the whole domain of the function. Here we have not to change the domain. Click Evaluate then OK.

Figure 43 -Choosing a domain for the derivative

Note Casyopée’s diagnostic about the sign of the new function.

Figure 44 - Diagnosing the sign of a function

The derivative appears in the *Notepad* and in the *function list* (as a child of the function *f*). Its formula is displayed in the *expression list*. The symbolic calculation tools of the **Calculate** menu allows to obtain equivalent expressions of the derivative.

Figure 45 - Derivative

### Solving an equation

In the Algebra tab menu, choose **Create equation/ f(x)=k**. Enter the equation by choosing *f(x) =* in the list and entering* -2 in the box, then* click **Create**.

A new list displays at the bottom of the Algebra tab. It is the *equation list*.

**Figure ****47 - Equation list**

Click on the equation that you want to have the solutions (it is highlighted). Choose **Exact** and validate with **OK**.

The solutions appear in the *Notepad* and a *dialogue box* asks if the solutions must be put in the *X-values list*; click on **Yes**.

**Figure ****48 - Confirmation box for solutions of an equation Figure 49 - Solution of an equation in the X-values list**

You can easily read the results of the study in the NotePad.