Calculus 3 - Newton Raphson Method

Question

Hi there. Please help me solve this problem. I don't even know where to start. Thanks much.

Use the Newton-Raphson Method to show that x_n+1 = 2x_n³ + x_n² + 10 numerator

(3x_n² + 2x_n) denominator

Answer 1

The Newton-Raphson Method is used to find the irrational roots of equations.

In this case, I think, the question is: for what value of x is x³ + x² = 10.

Use the formula to solve this equation. You will need f'(x)!

Answer 2

Don't know where to start? How about your textbook, where it explains this method? Or google?

Recall that to find where f(x)=0, pick your first x_{n and then}

x_{n+1 =} x_{n - f(}x_n)/f''(x_n)

However, you have not said what f(x) is.