1. © Annie Patton Newton-Raphson Method Next Slide

2. © Annie Patton Aim of lesson To learn how the Newton- Raphson method can be used for finding non integer roots of a cubic equation. Next Slide

3. © Annie Patton Newton-Raphson Method Next Slide Newton-Raphson states that if x 1 is an approximation to a root of a cubic equation then x 2 is a more accurate result.

4. © Annie Patton Next Slide Leaving Certificate 2006 Higher Level Paper 1 no 7(a) Start clicking when you want to see the answer.

5. © Annie Patton (x 1, f(x 1 )) (x 1,0) (x 2,0) Proof of Newton-Raphson Method Next Slide

6. © Annie Patton Steps to using the Newton- Raphson Method The more times Step 4 is repeated the more accurate the answer. Next Slide

7. © Annie Patton Leaving Certificate 2007 Higher Level Paper 1 no 7(a) Start clicking when you want to see the answer. Next Slide

8. © Annie Patton Start clicking when you want to see the answer. Next Slide

9. © Annie Patton Leaving Certificate 2005 Higher Level Paper 1 no 7(c)(i)(ii) Start clicking when you want to see the answer. Quadratic Next Slide

10. © Annie Patton Leaving Certificate 2005 Higher Level Paper 1 no 7(c)(iii) Start clicking when you want to see the answer. Next Slide

11. © Annie Patton Leaving Certificate 2003 Higher Level Paper 1 no 6(b) Start clicking when you want to see the answer. Next Slide

12. © Annie Patton Leaving Certificate1998 Higher Level Paper 1 part no 7( c) Start clicking when you want to see the answer. Next Slide

13. © Annie Patton Next Slide Start clicking when you want to see the answer.

14. © Annie Patton Newton-Raphson states that if x 1 is an approximation to a root of a cubic equation then x 2 is a more accurate result. Next Slide

15. © Annie Patton Homework Leaving Certificate Higher Paper 1 No 7(a) Next Slide

16. © Annie Patton Steps to using the Newton- Raphson Method The more times Step 4 is repeated the more accurate the answer.