# Math Insight

### Applet: The derivative of a function

The function $f(x)$ is plotted by the thick blue curve. Its derivative $f'(x)$ is shown by the thin green curve. The large red diamond on the graph of $f$ represents a point $(x_0,f(x_0))$, and you can change $x_0$ by dragging this point with your mouse. A tangent line to $f$ calculated at $x=x_0$ is shown by the red line. Its slope is the derivative $f'(x_0)$ of $f$ evaluated at $x=x_0$. This slope is also displayed by the smaller red diamond on the graph of $f'$, which is at the point $(x_0,f'(x_0))$. As you change $x_0$, this smaller diamond representing the slope traces out the graph of the derivative. You can change $f(x)$ by typing a new value in its box. The value of $f'(x)$ is displayed to the right of the box. You can hide items by unchecking the corresponding check boxes in order to test yourself on how well you can determine the derivative from the function or vice versa.

You can use the buttons at the top to zoom in and out as well as pan the view.

Applet file: derivative_function.ggb

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This applet was created using Geogebra. In most Geogebra applets, you can move objects by dragging them with the mouse. In some, you can enter values with the keyboard. To reset the applet to its original view, click the icon in the upper right hand corner.

You can download the applet onto your own computer so you can use it outside this web page or even modify it to improve it. You simply need to download the above applet file and download the Geogebra program onto your own computer.