diff --git a/tests/function.rs b/tests/function.rs
index 42be887..c2623aa 100644
--- a/tests/function.rs
+++ b/tests/function.rs
@@ -271,3 +271,252 @@ fn middle_function() {
 fn right_function() {
     do_test(Riemann::Right, 0.8800000000000001);
 }
+
+#[test]
+fn test_extrema() {
+    let mut settings = app_settings_constructor(Riemann::Middle, -2.0, 2.0, 100, 100, -2.0, 2.0);
+    settings.do_extrema = true;
+
+    let mut function = FunctionEntry::default();
+    function.update_string("x^2 - 4"); // Parabola with vertex at (0, -4)
+    function.integral = false;
+    function.derivative = false;
+
+    function.calculate(true, true, false, settings);
+
+    // For f(x) = x^2 - 4, f'(x) = 2x
+    // Extrema occurs where f'(x) = 0, so at x = 0
+    assert!(!function.extrema_data.is_empty());
+
+    // Should have exactly one extremum at x = 0
+    assert_eq!(function.extrema_data.len(), 1);
+
+    let extremum = function.extrema_data[0];
+    assert!(emath::almost_equal(extremum.x as f32, 0.0, f32::EPSILON));
+    assert!(emath::almost_equal(extremum.y as f32, -4.0, f32::EPSILON));
+}
+
+#[test]
+fn test_extrema_multiple() {
+    let mut settings = app_settings_constructor(Riemann::Middle, -3.0, 3.0, 200, 200, -3.0, 3.0);
+    settings.do_extrema = true;
+
+    let mut function = FunctionEntry::default();
+    function.update_string("x^3 - 3*x"); // Cubic with local max and min
+    function.integral = false;
+    function.derivative = false;
+
+    function.calculate(true, true, false, settings);
+
+    // For f(x) = x^3 - 3x, f'(x) = 3x^2 - 3
+    // Extrema occur where f'(x) = 0, so at x = ±1
+    assert!(!function.extrema_data.is_empty());
+
+    // Should have exactly two extrema
+    assert_eq!(function.extrema_data.len(), 2);
+
+    // Sort by x coordinate for consistent testing
+    let mut extrema = function.extrema_data.clone();
+    extrema.sort_by(|a, b| a.x.partial_cmp(&b.x).unwrap());
+
+    // First extremum at x = -1, f(-1) = -1 + 3 = 2
+    assert!(emath::almost_equal(extrema[0].x as f32, -1.0, 0.01));
+    assert!(emath::almost_equal(extrema[0].y as f32, 2.0, 0.01));
+
+    // Second extremum at x = 1, f(1) = 1 - 3 = -2
+    assert!(emath::almost_equal(extrema[1].x as f32, 1.0, 0.01));
+    assert!(emath::almost_equal(extrema[1].y as f32, -2.0, 0.01));
+}
+
+#[test]
+fn test_extrema_disabled() {
+    let mut settings = app_settings_constructor(Riemann::Middle, -2.0, 2.0, 100, 100, -2.0, 2.0);
+    settings.do_extrema = false; // Disable extrema
+
+    let mut function = FunctionEntry::default();
+    function.update_string("x^2 - 4");
+    function.integral = false;
+    function.derivative = false;
+
+    function.calculate(true, true, false, settings);
+
+    // Extrema data should be empty when disabled
+    assert!(function.extrema_data.is_empty());
+}
+
+#[test]
+fn test_roots() {
+    let mut settings = app_settings_constructor(Riemann::Middle, -3.0, 3.0, 200, 200, -3.0, 3.0);
+    settings.do_roots = true;
+
+    let mut function = FunctionEntry::default();
+    function.update_string("x^2 - 4"); // Parabola crossing x-axis at ±2
+    function.integral = false;
+    function.derivative = false;
+
+    function.calculate(true, true, false, settings);
+
+    // For f(x) = x^2 - 4, roots occur where x^2 = 4, so at x = ±2
+    assert!(!function.root_data.is_empty());
+
+    // Should have exactly two roots
+    assert_eq!(function.root_data.len(), 2);
+
+    // Sort by x coordinate for consistent testing
+    let mut roots = function.root_data.clone();
+    roots.sort_by(|a, b| a.x.partial_cmp(&b.x).unwrap());
+
+    // First root at x = -2
+    assert!(emath::almost_equal(roots[0].x as f32, -2.0, 0.01));
+    assert!(emath::almost_equal(roots[0].y as f32, 0.0, 0.001));
+
+    // Second root at x = 2
+    assert!(emath::almost_equal(roots[1].x as f32, 2.0, 0.01));
+    assert!(emath::almost_equal(roots[1].y as f32, 0.0, 0.001));
+}
+
+#[test]
+fn test_roots_single() {
+    let mut settings = app_settings_constructor(Riemann::Middle, -2.0, 2.0, 100, 100, -2.0, 2.0);
+    settings.do_roots = true;
+
+    let mut function = FunctionEntry::default();
+    function.update_string("x - 1"); // Linear function crossing x-axis at x = 1
+    function.integral = false;
+    function.derivative = false;
+
+    function.calculate(true, true, false, settings);
+
+    // For f(x) = x - 1, root occurs at x = 1
+    assert!(!function.root_data.is_empty());
+
+    // Should have exactly one root
+    assert_eq!(function.root_data.len(), 1);
+
+    let root = function.root_data[0];
+    assert!(emath::almost_equal(root.x as f32, 1.0, 0.01));
+    assert!(emath::almost_equal(root.y as f32, 0.0, f32::EPSILON));
+}
+
+#[test]
+fn test_roots_disabled() {
+    let mut settings = app_settings_constructor(Riemann::Middle, -3.0, 3.0, 200, 200, -3.0, 3.0);
+    settings.do_roots = false; // Disable roots
+
+    let mut function = FunctionEntry::default();
+    function.update_string("x^2 - 4");
+    function.integral = false;
+    function.derivative = false;
+
+    function.calculate(true, true, false, settings);
+
+    // Root data should be empty when disabled
+    assert!(function.root_data.is_empty());
+}
+
+#[test]
+fn test_extrema_and_roots_together() {
+    let mut settings = app_settings_constructor(Riemann::Middle, -3.0, 3.0, 200, 200, -3.0, 3.0);
+    settings.do_extrema = true;
+    settings.do_roots = true;
+
+    let mut function = FunctionEntry::default();
+    function.update_string("x^2 - 1"); // Parabola with vertex at (0, -1) and roots at ±1
+    function.integral = false;
+    function.derivative = false;
+
+    function.calculate(true, true, false, settings);
+
+    // Should have one extremum at x = 0
+    assert!(!function.extrema_data.is_empty());
+    assert_eq!(function.extrema_data.len(), 1);
+    let extremum = function.extrema_data[0];
+    assert!(emath::almost_equal(extremum.x as f32, 0.0, 0.01));
+    assert!(emath::almost_equal(extremum.y as f32, -1.0, 0.01));
+
+    // Should have two roots at x = ±1
+    assert!(!function.root_data.is_empty());
+    assert_eq!(function.root_data.len(), 2);
+
+    let mut roots = function.root_data.clone();
+    roots.sort_by(|a, b| a.x.partial_cmp(&b.x).unwrap());
+
+    assert!(emath::almost_equal(roots[0].x as f32, -1.0, 0.01));
+    assert!(emath::almost_equal(roots[1].x as f32, 1.0, 0.01));
+}
+
+#[test]
+fn test_extrema_no_extrema() {
+    let mut settings = app_settings_constructor(Riemann::Middle, -2.0, 2.0, 100, 100, -2.0, 2.0);
+    settings.do_extrema = true;
+
+    let mut function = FunctionEntry::default();
+    function.update_string("x"); // Linear function has no extrema
+    function.integral = false;
+    function.derivative = false;
+
+    function.calculate(true, true, false, settings);
+
+    // Linear function should have no extrema
+    assert!(function.extrema_data.is_empty());
+}
+
+#[test]
+fn test_roots_no_roots() {
+    let mut settings = app_settings_constructor(Riemann::Middle, -2.0, 2.0, 100, 100, -2.0, 2.0);
+    settings.do_roots = true;
+
+    let mut function = FunctionEntry::default();
+    function.update_string("x^2 + 1"); // Parabola that never crosses x-axis
+    function.integral = false;
+    function.derivative = false;
+
+    function.calculate(true, true, false, settings);
+
+    // Function that never crosses x-axis should have no roots
+    assert!(function.root_data.is_empty());
+}
+
+#[test]
+fn test_extrema_and_roots_with_trig() {
+    let mut settings = app_settings_constructor(Riemann::Middle, -4.0, 4.0, 300, 300, -4.0, 4.0);
+    settings.do_extrema = true;
+    settings.do_roots = true;
+
+    let mut function = FunctionEntry::default();
+    function.update_string("sin(x)"); // Sine function has extrema at odd multiples of π/2
+    function.integral = false;
+    function.derivative = false;
+
+    function.calculate(true, true, false, settings);
+
+    // Sine function should have extrema in the given range
+    assert!(!function.extrema_data.is_empty());
+
+    // Should have multiple extrema (local max/min)
+    assert!(function.extrema_data.len() >= 2);
+
+    // Check that extrema are at approximately the right locations
+    // Local max at π/2 ≈ 1.57, local min at 3π/2 ≈ 4.71 (outside range)
+    // Local min at -π/2 ≈ -1.57, local max at -3π/2 ≈ -4.71 (outside range)
+    let extrema_x: Vec<f32> = function.extrema_data.iter().map(|p| p.x as f32).collect();
+
+    // Should have extrema near ±π/2
+    assert!(extrema_x
+        .iter()
+        .any(|&x| emath::almost_equal(x, std::f32::consts::PI / 2.0, 0.1)));
+    assert!(extrema_x
+        .iter()
+        .any(|&x| emath::almost_equal(x, -std::f32::consts::PI / 2.0, 0.1)));
+
+    let roots_x: Vec<f32> = function.root_data.iter().map(|p| p.x as f32).collect();
+
+    assert!(roots_x
+        .iter()
+        .any(|&x| emath::almost_equal(x, std::f32::consts::PI, 0.1)));
+    assert!(roots_x
+        .iter()
+        .any(|&x| emath::almost_equal(x, -std::f32::consts::PI, 0.1)));
+
+    assert!(roots_x.iter().any(|&x| emath::almost_equal(x, 0.0, 0.1)));
+}