Newton's method for your personal monic cubic

assignments

#1

(5 pts by Friday, January 25)

Continuing with your personal monic cubic, use out Newton’s method for complex polynomials tool to generate an image of the basins of attraction for Newton’s method as applied to your personal monic cubic.


#2

My personal monic cubic was f(x) = x^3 + 2x + 3.

Using the tool provided above, I generated the following image of the basins of attraction for Newton’s method of f(x):


#3

My personal cubic is x^3+2x^2+x+1, corresponding to the coefficients 1,1,2,1.

Thus, the basins of attraction for Newton’s Method appear as follows.


#4

Using Mark’s tool, I found that the basins of attraction for my polynomial f(x)=x^3=x^2-x+1 look like this:

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Pretty neat!


#5


#6

My personal monic cubic was f(x)=x^3+x^2+2x.
Using the tool provided, I get this image.


#7

My personal monic cubic is f(x) = x^3 + x, which generates the following Newton’s method plot: