diff --git a/maxima.py b/maxima.py
index ed03ef6..dbfb395 100644
--- a/maxima.py
+++ b/maxima.py
@@ -16,6 +16,12 @@ def find_maxima(x):
     idx = []
     for i in range(len(x)):
         # `i` is a local maximum if the signal decreases before and after it
-        if x[i-1] < x[i] and x[i+1] < x[i]:
+        if i == len(x) - 1:
+            if x[i-1] < x[i]:
+                idx.append(i)
+        elif i == 0:
+            if x[i] > x[i+1]:
+                idx.append(i)
+        elif x[i-1] < x[i] and x[i+1] < x[i]:
             idx.append(i)
     return idx
diff --git a/test_maxima.py b/test_maxima.py
new file mode 100644
index 0000000..b951cdf
--- /dev/null
+++ b/test_maxima.py
@@ -0,0 +1,85 @@
+import numpy as np
+
+from maxima import find_maxima
+
+def test_simple_sequence_two_maxima():
+    inp = [0, 1, 2, 1, 2, 1, 0]
+    out = find_maxima(inp)
+    exp = [2, 4]
+    assert exp == out
+
+def test_simple_sequence_one_maximum():
+    inp = [-i**2 for i in range(-3, 4)]
+    out = find_maxima(inp)
+    exp = [3]
+    assert exp == out
+
+def test_sine_wave():
+    inp = [np.sin(2*alpha) for alpha in np.linspace(0.0, 5.0, 100)]
+    out = find_maxima(inp)
+    exp = [16, 78]
+    assert exp == out
+
+def test_max_on_both_borders():
+    inp = [4, 2, 1, 3, 1, 2]
+    out = find_maxima(inp)
+    exp = [0, 3, 5]
+    assert exp == out
+
+def test_max_on_both_borders_and_absolute_max_on_right_border():
+    inp = [4, 2, 1, 3, 1, 5]
+    out = find_maxima(inp)
+    exp = [0, 3, 5]
+    assert exp == out
+
+def test_one_max_on_left_border():
+    inp = [4, 2, 1, 0, -1]
+    out = find_maxima(inp)
+    exp = [0]
+    assert exp == out
+
+def test_one_max_on_right_border():
+    inp = [-1, 0, 1, 2, 4]
+    out = find_maxima(inp)
+    exp = [4]
+    assert exp == out
+
+def test_plateau1():
+    inp = [1, 2, 2, 1]
+    out = find_maxima(inp)
+    exp = []
+    assert exp == out
+
+def test_plateau2():
+    inp = [1, 2, 2, 3, 1]
+    out = find_maxima(inp)
+    exp = [3]
+    assert exp == out
+
+def test_plateau3():
+    inp = [1, 3, 2, 2, 1]
+    out = find_maxima(inp)
+    exp = [1]
+    assert exp == out
+
+def test_plateau4():
+    inp = [3, 2, 2, 3]
+    out = find_maxima(inp)
+    exp = [0, 3]
+    assert exp == out
+
+
+# additional tests for
+# - max on both borders
+#   x = [4, 2, 1, 3, 1, 2]
+# - max on both borders, absolute max on right border
+#   x = [4, 2, 1, 3, 1, 5]
+# - one max (absolute) on left border
+#   x = [4, 2, 1, 3, 1]
+# - plateau
+#   x = [1, 2, 2, 1]
+#   (decide for a sensible output in this case)
+# - test cases for plateau
+#   x = [1, 2, 2, 3, 1]
+#   x = [1, 3, 2, 2, 1]
+#   x = [3, 2, 2, 3]