This spreadsheet demonstrates the calculation of the slopes of secants to a non-linear function which approximate the slope of a tangent at a given point on the curve of the function.
The function used here is . The secants are through the points and . Point is a fixed point at and point starts at and keeps moving closer to until it reaches . The rises and runs are calculated for each set of points and the slope is then calculated between and . As we see, the slope of the tangent between and equals .
We can make the reasonable conclusion that the slope of the tangent to this function at equals .