A secant line is a straight line joining two points on a function. It is also equivalent to the average rate of change, or simply the slope between two points.
A tangent line is a straight line that touches a function at only one point. The tangent line represents the instantaneous rate of change of the function at that one point. The slope of the tangent line at a point on the function is equal to the derivative of the function at the same point.
Let’s see what happens as the two points used for the secant line get closer to one another. Let Dx represent the distant between the two points along the x-axis and determine the limit as Dx approaches zero.
As the two points used for the secant line get closer to one another, the average rate of change becomes the instantaneous rate of change and the secant line becomes the tangent line.