The Limit of the Secant Line is the Tangent Line
Change the position of the green tangent point using the slider at the top. A tangent line is shown along with the value of its slope, the Instantaneous Rate of Change (IROC). Use the slider at the bottom to move the red point, which forms a secant line with the tangent point. The slope of the secant line is the Average Rate of Change (AROC). As the secant point moves toward the tangent point, the secant line becomes the tangent line. The AROC requires two distinct points to calculate, so when delta-x becomes zero, the secant line "disappears" and the AROC is undefined.