Derivative

derivative.cpp

@@ -0,0 +1,39 @@
+#include <iostream>
+#include <math.h>
+
+using namespace std;
+
+double derivative(double (*f)(double), double x, double epsilon) {
+    return (f(x + epsilon) - f(x)) / epsilon;
+}
+
+bool test_interval(double epsilon, double precision) {
+    for (double x = 0; x <= 3.14; x += 0.0001) {
+        double approx = derivative(sin, x, epsilon);
+        double precise = cos(x);
+        if (abs(approx - precise) > precision) {
+            return false;
+        }
+    }
+    return true;
+}
+
+int main() {
+    for (double e = 0.003; e > 0.001; e -= 0.000001) {
+        if (test_interval(e, 0.001)) {
+            cout << "Epsilon found: " << e << endl;
+            break;
+        }
+    }
+    double max_diff;
+    double max_x;
+    for (double x = 0; x <= 3.14; x += 0.0001) {
+        double diff = abs(derivative(sin, x, 0.002) - cos(x));
+        if (diff > max_diff) {
+            max_diff = diff;
+            max_x = x;
+        }
+    }
+    cout << "Max diff at " << max_x << " of " << max_diff << endl;
+    return 0;
+}