The slope of a tangent to a logarithm curve
See DescartesLog.html for how this curve was constructed.
Drag the slider to move the point at which the tangent is being computed.
Move points A_1 and H to adjust the shape of the logarithm curve.
To see the same results as a table, drag the divider to see the spreadsheet window at right.
The exact slope of the tangent to a curve defined algebraically as the graph of a function can be computed with calculus by taking the derivative. This diagram shows how to get the approximate slope, to as much precision as you like, without calculus.
Calculus uses the slope calculated using the center point and a point to the right or left, then takes a limit. But before you take the limit, the slope using the left and right points is much more accurate.