How do you use Newton's method to find the approximate solution to the equation #2x^3+x+4=0#?
1 Answer
Using N-R Iteration we get the solution is
Explanation:
Let
First let us look at the graphs:
graph{2x^3+x^2+4 [-4, 4, -10, 10]}
We can see there is one solution in the interval
We can find the solution numerically, using Newton-Rhapson method
# \ \ \ \ \ \ \f(x) = 2x^3+x^2+4 #
# :. f'(x) = 6x^2+2x #
The Newton-Rhapson method uses the following iterative sequence
# { (x_1,=-1), ( x_(n+1), = x_n - f(x_n)/(f'(x_n)) ) :} #
Then using excel working to 8dp we can tabulate the iterations as follows:
We could equally use a modern scientific graphing calculator as most new calculators have an " Ans " button that allows the last calculated result to be used as the input of an iterated expression.
And we conclude that the solution is