diff --git a/src/misc.rs b/src/misc.rs
index 3c62b5b..eae6bd2 100644
--- a/src/misc.rs
+++ b/src/misc.rs
@@ -253,8 +253,14 @@ pub fn newtons_method(
 ) -> Option<f64> {
 	let mut x1: f64 = *start_x;
 	let mut x2: f64;
+	let mut derivative: f64;
 	loop {
-		x2 = x1 - (f(x1) / f_1(x1));
+		derivative = f_1(x1);
+		if !derivative.is_finite() {
+			return None;
+		}
+
+		x2 = x1 - (f(x1) / derivative);
 		if !x2.is_finite() | !range.contains(&x2) {
 			return None;
 		}
diff --git a/tests/misc.rs b/tests/misc.rs
index a237002..7275117 100644
--- a/tests/misc.rs
+++ b/tests/misc.rs
@@ -201,4 +201,22 @@ fn newtons_method() {
 		&f64::EPSILON,
 	);
 	assert_eq!(data, None);
+
+	let data = newtons_method(
+		&|_: f64| f64::INFINITY,
+		&|x: f64| x.sin(),
+		&0.0,
+		&(-10.0..10.0),
+		&f64::EPSILON,
+	);
+	assert_eq!(data, None);
+
+	let data = newtons_method(
+		&|x: f64| x.sin(),
+		&|_: f64| f64::INFINITY,
+		&0.0,
+		&(-10.0..10.0),
+		&f64::EPSILON,
+	);
+	assert_eq!(data, None);
 }