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diff --git a/src/tests,approx.lisp b/src/tests,approx.lisp
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+(defpackage lizfcm/tests.approx
+  (:use :cl
+        :fiveam
+        :lizfcm.approx
+        :lizfcm.utils
+        :lizfcm/tests)
+  (:export :approx-suite))
+(in-package :lizfcm/tests.approx)
+
+(def-suite approx-suite
+           :in lizfcm-test-suite)
+(in-suite approx-suite)
+
+(test central-derivative-at
+      :description "derivative at is within bounds"
+      (let ((f (lambda (x) (* x x)))
+            (x 2)
+            (accepted-delta 0.02)
+            (f-prime-at-x 4)
+            (delta 0.01))
+        (is (within-range-p
+              (central-derivative-at f x delta)
+              f-prime-at-x
+              accepted-delta))))
+
+(test fwd-derivative-at
+      :description "forward derivative at is within bounds"
+      (let ((f (lambda (x) (* x x)))
+            (x 2)
+            (accepted-delta 0.02)
+            (f-prime-at-x 4)
+            (delta 0.01))
+        (is (within-range-p
+              (forward-derivative-at f x delta)
+              f-prime-at-x
+              accepted-delta))))
+
+(test bwd-derivative-at
+      :description "backward derivative at is within bounds"
+      (let ((f (lambda (x) (* x x)))
+            (x 2)
+            (accepted-delta 0.02)
+            (f-prime-at-x 4)
+            (delta 0.01))
+        (is (within-range-p
+              (backward-derivative-at f x delta)
+              f-prime-at-x
+              accepted-delta))))