diff --git a/cl/lizfcm.asd b/cl/lizfcm.asd
new file mode 100644
index 0000000..9e91eb0
--- /dev/null
+++ b/cl/lizfcm.asd
@@ -0,0 +1,29 @@
+(asdf:defsystem "lizfcm"
+                :version "0.1.0"
+                :author "Elizabeth Hunt"
+                :license "MIT"
+                :components ((:module "src"
+                                      :components
+                                      ((:module "utils"
+                                                :components
+                                                ((:file "within-range" :depends-on ("package"))
+                                                 (:file "package")))
+                                       (:module "approx"
+                                                :components
+                                                ((:file "derivative" :depends-on ("package"))
+                                                 (:file "package")))))))
+
+
+(asdf:defsystem "lizfcm/tests"
+                :author "Elizabeth Hunt"
+                :license "MIT"
+                :depends-on (:fiveam
+                              :lizfcm)
+                :components ((:module "tests"
+                                      :components
+                                      ((:file "approx" :depends-on ("suite"))
+                                       (:file "suite"))))
+                :perform (asdf:test-op (o c) (uiop:symbol-call
+                                               :fiveam :run!
+                                               (uiop:find-symbol* :lizfcm-test-suite :lizfcm/tests))))
+
diff --git a/cl/src/approx/derivative.lisp b/cl/src/approx/derivative.lisp
new file mode 100644
index 0000000..280463f
--- /dev/null
+++ b/cl/src/approx/derivative.lisp
@@ -0,0 +1,8 @@
+(in-package :lizfcm.approx)
+
+(defun derivative-at (f x &optional (delta 0.01))
+  (let* ((x2 (+ x delta))
+         (x1 (- x delta))
+         (y2 (apply f (list x2)))
+         (y1 (apply f (list x1))))
+    (/ (- y2 y1) (- x2 x1))))
diff --git a/cl/src/approx/package.lisp b/cl/src/approx/package.lisp
new file mode 100644
index 0000000..60dd0bb
--- /dev/null
+++ b/cl/src/approx/package.lisp
@@ -0,0 +1,4 @@
+(in-package :cl-user)
+(defpackage lizfcm.approx
+  (:use :cl)
+  (:export :derivative-at))
diff --git a/cl/src/utils/package.lisp b/cl/src/utils/package.lisp
new file mode 100644
index 0000000..0436a94
--- /dev/null
+++ b/cl/src/utils/package.lisp
@@ -0,0 +1,4 @@
+(in-package :cl-user)
+(defpackage lizfcm.utils
+  (:use :cl)
+  (:export :within-range-p))
diff --git a/cl/src/utils/within-range.lisp b/cl/src/utils/within-range.lisp
new file mode 100644
index 0000000..9a0b762
--- /dev/null
+++ b/cl/src/utils/within-range.lisp
@@ -0,0 +1,5 @@
+(in-package :lizfcm.utils)
+
+(defun within-range-p (x true-value delta)
+  (and (< x (+ true-value delta))
+       (> x (- true-value delta))))
diff --git a/cl/tests/approx.lisp b/cl/tests/approx.lisp
new file mode 100644
index 0000000..a458e66
--- /dev/null
+++ b/cl/tests/approx.lisp
@@ -0,0 +1,23 @@
+(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 derivative-at
+      :description "derivative at is within bounds"
+      (let ((f (lambda (x) (* x x)))
+            (x 2)
+            (f-prime-at-x 4)
+            (delta 0.01))
+        (is (within-range-p
+              (derivative-at f x delta)
+              f-prime-at-x
+              0.1))))
diff --git a/cl/tests/suite.lisp b/cl/tests/suite.lisp
new file mode 100644
index 0000000..e23cfaf
--- /dev/null
+++ b/cl/tests/suite.lisp
@@ -0,0 +1,10 @@
+(in-package :cl-user)
+(defpackage lizfcm/tests
+  (:use :cl
+        :fiveam)
+  (:export :run!
+           :lizfcm-test-suite))
+(in-package :lizfcm/tests)
+
+(def-suite lizfcm-test-suite
+    :description "The ultimate parent test suite")