See DescartesLog.html for how this curve was constructed.

Drag the slider to move the point at which the tangent is being computed.[br]Move points A_1 and H to adjust the shape of the logarithm curve.[br]To see the same results as a table, drag the divider to see the spreadsheet window at right.[br][br]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.[br][br]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.