Slope of Secant versus Tangent
- Ben Babcock
Fix a point A on the function f, and let B be any other point on the function. Then as the distance between A and B approaches zero, the slope of the secant line approaches the slope of the tangent line.
Drag B along the function and observe how the slope of the secant line changes. Use the checkbox to display the tangent line and its slope when you want to compare. What happens to the slope of the secant line if you move B so that it's on top of A? You can also change the definition of f to observe how this works for other functions. The default definition of f simply gives a pleasing visual shape for the demonstration.