linear approximation of function in MMA

interpolationLinearApprox.m

xMax = 1.4;
numPartitions = 10; dx = xMax/numPartitions;
pointsAndLines[pts_] := {Point@pts, Line@pts};
fun[x_] := x^2;
Plot[fun@x, {x, 0, xMax},
  PlotRange -> All, PlotStyle -> Directive[Thick], Frame -> True, 
  GridLines -> Automatic, 
  FrameStyle -> Directive[Black, Thick, Large], 
  PlotLegends -> "Expressions",
  ImageSize -> 500
  ]~Show~Graphics[{
   [email protected], 
   pointsAndLines[
    Thread@{# dx, Accumulate[dx fun'[(# - 1) dx]]} &@
      Table[k, {k, 1, numPartitions}] // Prepend@{0, 0}]
   }]