Draw tangent to point in ListLinePLot

Question

I am using ListLinePlot to draw a number of points to a graph:

ListLinePlot[{{5 10^-3, 0}, {4.65 10^-3, 100}, {4.32 10^-3, 200}, {3.74 10^-3, 400}, 
    {3.23 10^-3, 600}, {2.6 10^-3, 900}, {2.09 10^-3, 1200}, {1.68 10^-3, 1500}}]

How can I also draw the tangent to the line in a point?

Answer 1

You can use Interpolation[] to reckon out tangent lines to your data, as in the following:

data = {{5 10^-3, 0}, {4.65 10^-3, 100}, {4.32 10^-3, 200},
        {3.74 10^-3, 400}, {3.23 10^-3, 600}, {2.6 10^-3, 900},
        {2.09 10^-3, 1200}, {1.68 10^-3, 1500}};

dint = Interpolation[data];
slope = dint';

With[{x = .003 (* where to draw the tangent *), h = 800 (* length of tangent *)},
 y = dint[x]; dir = Normalize[{1, slope[x]}]/2;
 ListLinePlot[data, Epilog -> Line[{{x, y} - h dir, {x, y} + h dir}]]]

---

If multiple tangents are desired, here's one way to go about it:

With[{pos = {.002, .003, .0045} (* where to place tangents *),
      h = 400 (* length of tangent *)},
 ListLinePlot[data, Axes -> None, Epilog -> 
   Table[With[{y = dint[x], dir = Normalize[{1, slope[x]}]/2},
              {AbsoluteThickness[2], Line[{{x, y} - h dir, {x, y} + h dir}]}],
         {x, pos}], Frame -> True, PlotStyle -> AbsoluteThickness[1]]]