This geogebra app shows tangents to a non-linear function for [math] 0 \le x \le 6.5[/math]. Note: it will take a while to load. Please be patient.
Click on the button in the bottom left corner of the app. Point A moves along the curve and the tangent line moves with it, always touching the curve as point A moves along. You can stop the motion at any place you wish to see what the slope of the tangent line is at that point. The methods of derivative calculus allow us to determine the slope of the tangent to curves of functions or relations.