Differentiation from First Principles
Graph 1: Decreasing the horizontal distance between two points
The horizontal distance between the two points is given by . Use the slider to change the value of . Decreasing the value of will bring the two points closer together.
You will notice as decreases and approaches zero, the line between the two points approaches the tangent of the curve at .
Therefore we can say that as , the gradient of the secant will approach the gradient of the function at .