diff --git a/pyomo/contrib/ampl_function_demo/build.py b/pyomo/contrib/ampl_function_demo/build.py
index 10b9667aded..2bb50ab203a 100644
--- a/pyomo/contrib/ampl_function_demo/build.py
+++ b/pyomo/contrib/ampl_function_demo/build.py
@@ -15,10 +15,10 @@
 
 def build_ampl_function_demo(user_args=[], parallel=None):
     return build_cmake_project(
-        targets=['src'],
-        package_name='asl_external_demo',
-        description='AMPL External function demo library',
-        user_args=['-DBUILD_AMPLASL_IF_NEEDED=ON'] + user_args,
+        targets=["src"],
+        package_name="asl_external_demo",
+        description="AMPL External function demo library",
+        user_args=["-DBUILD_AMPLASL_IF_NEEDED=ON"] + user_args,
         parallel=parallel,
     )
 
diff --git a/pyomo/contrib/ampl_function_demo/plugins.py b/pyomo/contrib/ampl_function_demo/plugins.py
index b06dc08614c..1887ebe0194 100644
--- a/pyomo/contrib/ampl_function_demo/plugins.py
+++ b/pyomo/contrib/ampl_function_demo/plugins.py
@@ -14,4 +14,4 @@
 
 
 def load():
-    ExtensionBuilderFactory.register('ampl_function_demo')(AMPLFunctionDemoBuilder)
+    ExtensionBuilderFactory.register("ampl_function_demo")(AMPLFunctionDemoBuilder)
diff --git a/pyomo/contrib/ampl_function_demo/src/functions.c b/pyomo/contrib/ampl_function_demo/src/functions.c
index fd4372693e7..1c4b3786677 100644
--- a/pyomo/contrib/ampl_function_demo/src/functions.c
+++ b/pyomo/contrib/ampl_function_demo/src/functions.c
@@ -159,6 +159,27 @@ extern real scbrt(arglist *al){
 }
 
 
+/* A function where f(x) = sgn(x)x^2  
+ */
+extern real sgnsqr(arglist *al){
+   real x = al->ra[al->at[0]];
+
+   real y = copysign(x * x, x);
+
+   // Compute the first derivative, if requested.
+   if (al->derivs!=NULL) {
+      al->derivs[0] = copysign(1, x) * 2 * x;
+   }
+
+   // Compute the second derivative, if requested.
+   if (al->hes!=NULL) {
+      al->hes[0] = copysign(2, x);
+   }
+
+   return y;
+}
+
+
 // Register external functions defined in this library with the ASL
 void funcadd(AmplExports *ae){
     /* Arguments for addfunc (this is not fully detailed; see funcadd.h)
@@ -173,6 +194,8 @@ void funcadd(AmplExports *ae){
      */
     addfunc("safe_cbrt", (rfunc)scbrt,
             FUNCADD_REAL_VALUED, 1, NULL);
+    addfunc("sgnsqr", (rfunc)sgnsqr,
+            FUNCADD_REAL_VALUED, 1, NULL);
     addfunc("demo_function", (rfunc)demo_function,
             FUNCADD_REAL_VALUED|FUNCADD_STRING_ARGS, -2, NULL);
 }
diff --git a/pyomo/contrib/ampl_function_demo/tests/test_ampl_function_demo.py b/pyomo/contrib/ampl_function_demo/tests/test_ampl_function_demo.py
index 196d6b2f4e9..2ba8b360bca 100644
--- a/pyomo/contrib/ampl_function_demo/tests/test_ampl_function_demo.py
+++ b/pyomo/contrib/ampl_function_demo/tests/test_ampl_function_demo.py
@@ -17,12 +17,12 @@
 from pyomo.core.base.external import nan
 
 flib = find_library("asl_external_demo")
-is_pypy = platform.python_implementation().lower().startswith('pypy')
+is_pypy = platform.python_implementation().lower().startswith("pypy")
 
 
 @unittest.skipUnless(flib, 'Could not find the "asl_external_demo.so" library')
 class TestAMPLExternalFunction(unittest.TestCase):
-    @unittest.skipIf(is_pypy, 'Cannot evaluate external functions under pypy')
+    @unittest.skipIf(is_pypy, "Cannot evaluate external functions under pypy")
     def test_eval_function(self):
         m = pyo.ConcreteModel()
         m.tf = pyo.ExternalFunction(library=flib, function="demo_function")
@@ -34,7 +34,7 @@ def test_eval_function(self):
             m.cbrt.evaluate_fgh([0]), (0, [100951], [-1.121679e13]), reltol=1e-5
         )
 
-    @unittest.skipIf(is_pypy, 'Cannot evaluate external functions under pypy')
+    @unittest.skipIf(is_pypy, "Cannot evaluate external functions under pypy")
     def test_eval_function_fgh(self):
         m = pyo.ConcreteModel()
         m.tf = pyo.ExternalFunction(library=flib, function="demo_function")
@@ -52,7 +52,7 @@ def test_eval_function_fgh(self):
         )
 
     @unittest.skipUnless(
-        check_available_solvers('ipopt'), "The 'ipopt' solver is not available"
+        check_available_solvers("ipopt"), "The 'ipopt' solver is not available"
     )
     def test_solve_function(self):
         m = pyo.ConcreteModel()
@@ -68,3 +68,18 @@ def test_solve_function(self):
         solver = pyo.SolverFactory("ipopt")
         solver.solve(m, tee=True)
         self.assertAlmostEqual(m.x(), 6, 4)
+
+    @unittest.skipIf(is_pypy, "Cannot evaluate external functions under pypy")
+    def test_eval_sqnsqr_function_fgh(self):
+        m = pyo.ConcreteModel()
+        m.tf = pyo.ExternalFunction(library=flib, function="sgnsqr")
+
+        f, g, h = m.tf.evaluate_fgh((2,))
+        self.assertEqual(f, 4)
+        self.assertEqual(g, [4])
+        self.assertEqual(h, [2])
+
+        f, g, h = m.tf.evaluate_fgh((-2,))
+        self.assertAlmostEqual(f, -4)
+        self.assertStructuredAlmostEqual(g, [4])
+        self.assertStructuredAlmostEqual(h, [-2])