f[x_] := 4 - x^2

vector[tail : {_, _}, slope_, length_: 1.] :=
  Module[{θ = ArcTan[slope]}, {tail, tail + length {Cos[θ], Sin[θ]}}]

tangetVectors = N @ Table[vector[{x, f[x]}, f'[x], .5], {x, Subdivide[-2, 2, 8]}]

{{{-2., 0.}, {-1.87873, 0.485071}},
 {{-1.5, 1.75}, {-1.34189, 2.22434}},
 {{-1., 3.}, {-0.776393, 3.44721}},
 {{-0.5, 3.75}, {-0.146447, 4.10355}},
 {{0., 4.}, {0.5, 4.}},
 {{0.5, 3.75}, {0.853553, 3.39645}},
 {{1., 3.}, {1.22361, 2.55279}},
 {{1.5,1.75}, {1.65811, 1.27566}},
 {{2., 0.}, {2.12127, -0.485071}}}

Plot[f[x], {x, -2, 2},
  AspectRatio -> 1,
  PlotStyle -> {Red, Dotted},
  PlotRangePadding -> {{Automatic, .2}, {.5, Automatic}},
  Epilog -> {AbsoluteThickness[1.5], Arrow /@ tangetVectors}]

Graphics[{AbsoluteThickness[1.75], Arrow /@ tangetVectors}]