Use Newton's method to find xsubscript6, when xsubscript0 = -7, for the function f(x) = x^2 + 13.5x + 45.

Question

anonymous · Answer

Newton's method states $$x _{1}= x _{0} - f(x _{0})/f'(x _{0})$$
So, to begin we shall evaluate the function for $$f(x _{0})$$ = 45.
We also need to find the first derivative and evaluate it at x = 0.
$$f'(x) = 2x + 13.5$$
So $$f'(x _{0})$$ = 13.5
Substitution all that into Newton's method gives us x1 = 7 - 45/23.5
So x1 = 3 2/3

Now to continue we can use the same process over with the variation of the original formula$$x _{n+1} = x _{n} - f (x_{n})/f'(x _{n})$$

It's a bit of work to get up to x6.