The equation x^3 – x^2 + 4x – 4 = 0 is to be solved using the Newton-Raphson method. If x =2 is taken as the initial approximation of the solution, then the next approximation using the method will be
- A. 2/3
- B. 4/3
- C. 1/3
- D. 5/3
Answer: B. 4/3
Explanation: f(2) = 2³ − 2² + 4(2) − 4 = 8; f'(x) = 3x² − 2x + 4, so f'(2) = 12. Then x₁ = x₀ − f(x₀)/f'(x₀) = 2 − 8/12 = 4/3.