Newton-Raphson Method

ALGORITHM: Newton-Raphson Method for Finding Roots INPUT: - Function f(x) - Derivative f'(x) - Initial guess x₀ - Tolerance ε (epsilon) - Maximum iterations N OUTPUT: - Approximate root xₙ - Number of iterations Step 1: START Step 2: Set iteration count i = 0 Step 3: Input initial guess x₀ Step 4: Input tolerance value ε (e.g., 0.00001) Step 5: Input maximum iterations N (e.g., 100) Step 6: DO WHILE i < N Step 6.1: Calculate f(xᵢ) and f'(xᵢ) Step 6.2: IF |f'(xᵢ)| < ε THEN Print "Derivative i