diff --git a/docs/src/extrapolation_methods.md b/docs/src/extrapolation_methods.md
index fbce5d0f..488746e8 100644
--- a/docs/src/extrapolation_methods.md
+++ b/docs/src/extrapolation_methods.md
@@ -26,8 +26,8 @@ This extrapolation type extends the interpolation with the boundary values of th
 ```@example tutorial
 A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.constant)
 plot(A)
-plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
-plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
 
 ## `ExtrapolationType.linear`
@@ -37,8 +37,8 @@ This extrapolation type extends the interpolation with a linear continuation of
 ```@example tutorial
 A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.linear)
 plot(A)
-plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
-plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
 
 ## `ExtrapolationType.extension`
@@ -85,6 +85,6 @@ You can also have different extrapolation types left and right of the data.
 A = QuadraticSpline(u, t; extrapolation_left = ExtrapolationType.reflective,
     extrapolation_right = ExtrapolationType.periodic)
 plot(A)
-plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
-plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
diff --git a/src/derivatives.jl b/src/derivatives.jl
index 7ee8fe2e..e7ed9cb3 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -1,9 +1,9 @@
 function derivative(A, t, order = 1)
     (order ∉ (1, 2)) && throw(DerivativeNotFoundError())
     if t < first(A.t)
-        _extrapolate_derivative_down(A, t, order)
+        _extrapolate_derivative_left(A, t, order)
     elseif t > last(A.t)
-        _extrapolate_derivative_up(A, t, order)
+        _extrapolate_derivative_right(A, t, order)
     else
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
@@ -13,16 +13,16 @@ function derivative(A, t, order = 1)
     end
 end
 
-function _extrapolate_derivative_down(A, t, order)
+function _extrapolate_derivative_left(A, t, order)
     (; extrapolation_left) = A
-    typed_zero = zero(first(A.u) / one(A.t[1]))
     if extrapolation_left == ExtrapolationType.none
         throw(LeftExtrapolationError())
     elseif extrapolation_left == ExtrapolationType.constant
-        typed_zero
+        zero(first(A.u) / one(A.t[1]))
     elseif extrapolation_left == ExtrapolationType.linear
-        (order == 1) ? derivative(A, first(A.t)) : typed_zero
-    elseif extrapolation_left == ExtrapolationType.extension
+        (order == 1) ? derivative(A, first(A.t)) : zero(first(A.u) / one(A.t[1]))
+    else
+        # extrapolation_left == ExtrapolationType.extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
@@ -38,16 +38,16 @@ function _extrapolate_derivative_down(A, t, order)
     end
 end
 
-function _extrapolate_derivative_up(A, t, order)
+function _extrapolate_derivative_right(A, t, order)
     (; extrapolation_right) = A
-    typed_zero = zero(first(A.u) / one(A.t[1]))
     if extrapolation_right == ExtrapolationType.none
         throw(RightExtrapolationError())
     elseif extrapolation_right == ExtrapolationType.constant
-        typed_zero
+        zero(first(A.u) / one(A.t[1]))
     elseif extrapolation_right == ExtrapolationType.linear
-        (order == 1) ? derivative(A, last(A.t)) : typed_zero
-    elseif extrapolation_right == ExtrapolationType.extension
+        (order == 1) ? derivative(A, last(A.t)) : zero(first(A.u) / one(A.t[1]))
+    else
+        # extrapolation_right == ExtrapolationType.extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
diff --git a/src/integrals.jl b/src/integrals.jl
index 6948f8f9..baabc634 100644
--- a/src/integrals.jl
+++ b/src/integrals.jl
@@ -24,11 +24,11 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
     if t1 < first(A.t)
         if t2 < first(A.t)
             # If interval is entirely below data
-            return _extrapolate_integral_down(A, t2) - extrapolate_integral_down(A.t1)
+            return _extrapolate_integral_left(A, t2) - extrapolate_integral_left(A.t1)
         end
 
         idx1 -= 1 # Make sure lowest complete interval is included
-        total += _extrapolate_integral_down(A, t1)
+        total += _extrapolate_integral_left(A, t1)
     else
         total += _integral(A, idx1, t1, A.t[idx1 + 1])
     end
@@ -37,11 +37,11 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
     if t2 > last(A.t)
         if t1 > last(A.t)
             # If interval is entirely above data
-            return _extrapolate_integral_up(A, t2) - extrapolate_integral_up(A.t, t1)
+            return _extrapolate_integral_right(A, t2) - extrapolate_integral_right(A.t, t1)
         end
 
         idx2 += 1 # Make sure highest complete interval is included
-        total += _extrapolate_integral_up(A, t2)
+        total += _extrapolate_integral_right(A, t2)
     else
         total += _integral(A, idx2, A.t[idx2], t2)
     end
@@ -65,7 +65,7 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
     return total
 end
 
-function _extrapolate_integral_down(A, t)
+function _extrapolate_integral_left(A, t)
     (; extrapolation_left) = A
     if extrapolation_left == ExtrapolationType.none
         throw(LeftExtrapolationError())
@@ -99,7 +99,7 @@ function _extrapolate_integral_down(A, t)
     end
 end
 
-function _extrapolate_integral_up(A, t)
+function _extrapolate_integral_right(A, t)
     (; extrapolation_right) = A
     if extrapolation_right == ExtrapolationType.none
         throw(RightExtrapolationError())
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index a0437b02..d7cab62a 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -1,14 +1,14 @@
 function _interpolate(A, t)
     if t < first(A.t)
-        _extrapolate_down(A, t)
+        _extrapolate_left(A, t)
     elseif t > last(A.t)
-        _extrapolate_up(A, t)
+        _extrapolate_right(A, t)
     else
         _interpolate(A, t, A.iguesser)
     end
 end
 
-function _extrapolate_down(A, t)
+function _extrapolate_left(A, t)
     (; extrapolation_left) = A
     if extrapolation_left == ExtrapolationType.none
         throw(LeftExtrapolationError())
@@ -30,7 +30,7 @@ function _extrapolate_down(A, t)
     end
 end
 
-function _extrapolate_up(A, t)
+function _extrapolate_right(A, t)
     (; extrapolation_right) = A
     if extrapolation_right == ExtrapolationType.none
         throw(RightExtrapolationError())
diff --git a/test/extrapolation_tests.jl b/test/extrapolation_tests.jl
index fa12be1b..12f7b2bb 100644
--- a/test/extrapolation_tests.jl
+++ b/test/extrapolation_tests.jl
@@ -50,7 +50,7 @@ end
     test_extrapolation(LinearInterpolation, u, t)
 
     for extrapolation_type in [ExtrapolationType.linear, ExtrapolationType.extension]
-        # Down extrapolation
+        # Left extrapolation
         A = LinearInterpolation(u, t; extrapolation_left = extrapolation_type)
         t_eval = 0.0
         @test A(t_eval) == 0.0
@@ -59,7 +59,7 @@ end
         @test DataInterpolations.integral(A, t_eval) == -0.5
         t_eval = 3.0
 
-        # Up extrapolation
+        # Right extrapolation
         A = LinearInterpolation(u, t; extrapolation_right = extrapolation_type)
         t_eval = 3.0
         @test A(t_eval) == 3.0
@@ -76,7 +76,7 @@ end
 
     test_extrapolation(QuadraticInterpolation, u, t)
 
-    # Linear down extrapolation
+    # Linear left extrapolation
     A = QuadraticInterpolation(u, t; extrapolation_left = ExtrapolationType.linear)
     t_eval = 0.0
     @test A(t_eval) ≈ -2.5
@@ -84,7 +84,7 @@ end
     @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
     @test DataInterpolations.integral(A, t_eval) ≈ 0.75
 
-    # Linear up extrapolation
+    # Linear right extrapolation
     A = QuadraticInterpolation(u, t; extrapolation_right = ExtrapolationType.linear)
     t_eval = 4.0
     @test A(t_eval) ≈ -0.5
@@ -92,7 +92,7 @@ end
     @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
     @test DataInterpolations.integral(A, t[end], t_eval) ≈ 0.75
 
-    # Extension down extrapolation
+    # Extension left extrapolation
     f = t -> (-3t^2 + 13t - 8) / 2
     df = t -> (-6t + 13) / 2
     A = QuadraticInterpolation(u, t; extrapolation_left = ExtrapolationType.extension)
@@ -102,7 +102,7 @@ end
     @test DataInterpolations.derivative(A, t_eval, 2) == -3
     @test DataInterpolations.integral(A, t_eval) ≈ 1.25
 
-    # Extension up extrapolation
+    # Extension right extrapolation
     A = QuadraticInterpolation(u, t; extrapolation_right = ExtrapolationType.extension)
     t_eval = 4.0
     @test A(t_eval) ≈ -2.0