To get around the problem in the previous activity, we're going to take a short cut with Geogebra. Geogebra has a tool built in for calculating the line at the limit of the secant lines. The line at the limit of the secant lines is called a [b]tangent line.[/b] We'll define it precisely in the next activity. For now, we're only going to see how Geogebra can calculate them for us..[br][br]The built-in tool in Geogebra for finding tangent lines is called "Tangents" and the icon looks like this: [icon]/images/ggb/toolbar/mode_tangent.png[/icon][br][br]Hunt around in the drop down menus for the Tangents tool, and use it to create the tangent line to [code]f(x)[/code] at [code]A[/code]. When you select it, it should provide you with instructions about how to use it. If not, leave your mouse hovered over the Geogebra tool for a quick set of instructions on how to use it.

The key thing to know is that the tangent line to a function [code]f(x)[/code] at a point [code]A[/code] like above is the limit of the secant lines at [code]A[/code] as [code]h[/code] tends to 0. Go back and review the [url=https://www.geogebra.org/m/x39ys4d7#chapter/398514]chapter on limits[/url] if you need to! By using this tool in Geogebra, we're taking a huge shortcut and letting the computer take care of calculating a pile of limits all at once. Pretty impressive. Move ahead to continue studying tangent lines.