diff --git a/maxima.py b/maxima.py
index ed03ef6..563d4cb 100644
--- a/maxima.py
+++ b/maxima.py
@@ -13,9 +13,20 @@ def find_maxima(x):
         idx -- list of indices of the local maxima in x
     """
 
+    if not isinstance(x, list):
+        raise ValueError
+
+    if not all(isinstance(_x, (int, float)) for _x in x):
+        raise ValueError
+
     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 == 0 and x[i + 1] < x[i])
+            or (i == len(x)-1 and x[i - 1] < x[i])
+            or (0 < i < len(x)-1 and 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..c1c2914
--- /dev/null
+++ b/test_maxima.py
@@ -0,0 +1,41 @@
+import maxima
+
+import pytest
+
+
+def test_left_boundary():
+    inp = [1, 0]
+    assert maxima.find_maxima(inp) == [0]
+
+
+def test_right_boundary():
+    inp = [0, 1]
+    assert maxima.find_maxima(inp) == [1]
+
+
+def test_both_boundaries():
+    inp = [2, 0, 1]
+    assert maxima.find_maxima(inp) == [0, 2]
+
+
+def test_both_boundaries_oob():
+    inp = [1, 0, 2]
+    assert maxima.find_maxima(inp) == [0, 2]
+
+
+def test_characters():
+    inp = "bca"
+    with pytest.raises(ValueError):
+        maxima.find_maxima(inp)
+
+
+def test_characters2():
+    inp = ["b", "c", "a"]
+    with pytest.raises(ValueError):
+        maxima.find_maxima(inp)
+
+
+def test_non_numeric():
+    inp = [None, [], "a", 5]
+    with pytest.raises(ValueError):
+        maxima.find_maxima(inp)