diff --git a/Project.toml b/Project.toml
index e4f7aa67..ab15e6db 100644
--- a/Project.toml
+++ b/Project.toml
@@ -7,6 +7,7 @@ version = "0.17.3"
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 FastGaussQuadrature = "442a2c76-b920-505d-bb47-c5924d526838"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
diff --git a/src/BSplineKit.jl b/src/BSplineKit.jl
index f23be67e..78e96a0d 100644
--- a/src/BSplineKit.jl
+++ b/src/BSplineKit.jl
@@ -2,7 +2,8 @@ module BSplineKit
 
 using Reexport
 using PrecompileTools
-using LinearAlgebra: LinearAlgebra  # needed for docs
+using LinearAlgebra: LinearAlgebra
+using ForwardDiff  # needed for docs
 
 include("BandedTensors/BandedTensors.jl")
 @reexport using .BandedTensors
diff --git a/src/SplineExtrapolations/SplineExtrapolations.jl b/src/SplineExtrapolations/SplineExtrapolations.jl
index 4496952e..2f923872 100644
--- a/src/SplineExtrapolations/SplineExtrapolations.jl
+++ b/src/SplineExtrapolations/SplineExtrapolations.jl
@@ -41,14 +41,13 @@ struct Linear <: AbstractExtrapolationMethod end
 function extrapolate_at_point(::Linear, S::Spline, x)
     a, b = boundaries(basis(S))
     if x < a
-        slope = (S(a + eps()) - S(a)) / eps()
+        slope = ForwardDiff.derivative(S, a)
         S(a) + slope * (x - a)
     elseif x > b
-        slope = (S(b) - S(b - eps())) / eps()
+        slope = ForwardDiff.derivative(S, b)
         S(b) + slope * (x - b)
     else
-        x′ = clamp(x, a, b)
-        S(x′)
+        S(x)
     end
 end