The tangent line problem deals with how to determine the slope of a non-straight function at a specific point, [math]\left( x, f\left(x\right) \right)[/math]. We can approximate that slope using the slope of a secant line through the point and a second point that we pick to be reasonably close to the first point.[br][br]In this applet you can choose any [math]x[/math]-value you like in the range [math]\left[ -3.6,3.6 \right][/math]. Then you can let [math]\Delta x[/math] vary from -1 to +1 using the slider. The value [math]\Delta x[/math] chooses how far away the second point is from our point of interest.[br][br]Notice that as [math]\Delta x[/math] approaches 0, from either the left or the right, the slope of the secant line gets closer to the desired slope of the tangent line. In Chapter 2 we'll talk about how to consider what happens as [math]\Delta x[/math] gets infinitely small.