Slope between Two Points on a Curve
Calculate the slope between two points on one of three curves by dragging the locators. As the locators get close enough, the slope gets closer to the slope of the tangent line, which is the value of the derivative of the function at the point.
The slope between two points, joined in the diagram by an arrow is calculated. The tangent at the point at the base of the arrow is calculated from the derivative of the function. The tangent line is shown in green.
It can be seen with a suitable choice of parameters that:
a straight line has a constant slope, and
the slope between two points approaches the tangent, as the distance between the points decreases.