The curve y equals x squared with a chosen base point. In zoom mode a slider narrows the window around the point; the curve visibly straightens into the tangent line, and a readout shows the window half-width and the gap between curve and line at the window's edge, which is the half-width squared and so shrinks much faster. In shrink-the-step mode a second point sits a step delta x to the right, joined to the base point by a secant line; a slider shrinks the step, and readouts show the rise, the run, and rise over run, which is always exactly two times the base point plus delta x and settles onto the slope two x as the step shrinks.

Zoom in until it’s straight

The curve y = x². Zoom in at a point and it becomes a line; or keep the view fixed, shrink the step, and watch rise ÷ run settle.