Consider the function

f(x) = 5x

and the tangent line at x = 0. Zoom in until the graphs of both appear to coincide and estimate the slope of the tangent line from the graph of f.


[Press here to see animation again!]

The slope of the line is approximately

(1.0405 - 0.96282)/(0.024571 + 0.02303) = 1.63

The slope of the tangent line can be shown to be ln( 5) = 1.609....

The animation was generated using graphs from JKGraph and GifGifGif.