How to Find Stationary Points in GeoGebra

You can use GeoGebra to find the stationary points of a function. One method involves using CAS. Another way is to use Algebra View and Graphics View.

Recall that Solve GeoGebra icon yields exact answers (fractions and roots), while Solve Numerically GeoGebra icon yields approximated answers given as decimal numbers.

GeoGebra Instruction 1

Stationary Points in CAS

Open CAS under GeoGebra icon View in GeoGebra icon Menu.
Input your function using f(x):=. Then press Enter.
To differentiate your function, click the expression in the previous row so that it is copied to the current one. Select the Derivative GeoGebra icon tool.
Click the expression of the derivative. Type =0 after the expression and press Solve GeoGebra icon or Solve Numerically GeoGebra icon.
To find the coordinates of the maxima and minima, you need to calculate the corresponding y-values. To do this, type f(x-value) and then press Enter. Do this for all the x-values you have found.
To determine visually if a point is a maximum, minimum or inflection point, you can look at the graph displayed in Graphics View.

CAS being used to find the zeros of the derivative of a function

If you only want to find the extrema (maxima or minima) of a function, you can just use Graphics View.

GeoGebra Instruction 2

Extrema in Graphics View

Open Algebra View and Graphics View under GeoGebra icon View in GeoGebra icon Menu.
Enter your function into Algebra View and then press Enter.
To find the extrema of the function, type

Extremum(<Function>, <Start x-Value>, <End x-Value>)

in Algebra View.

Enter the function name (f(x), g(x), and so on) for <Function>. For <Start> and <End>, choose a sufficient interval based on the plotted graph. For <Start>, choose an x-value to the left of all the extrema of the graph, and for <End>, choose an x-value to the right of all the extrema of the graph.

Screenshot of GeoGebra showing the stationary points of a cubic polynomial

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