Ricky_Bobby

Here is a cool visual I have made in Mathematica that gives you a slider to watch Newton's method work. Just take the semi-colons off the end of the lines if you want to see individual output.

```
Clear[h]
Clear[n]
h[x_] := h[x] = 3 x^3 - 1
start = 4;
n[x_] := n[x] = x - ((h[x]/h'[x]))
list = NestList[n, start, 6];
pointlist = Table[ListPlot[{{list[[int]], h[list[[int]]]}}, PlotStyle -> PointSize[Medium]], {int, 1, Length[list], 1}];
linelist = Table[y = h[list[[step]]] + h'[list[[step]]] (x - list[[step]]), {step, 1, Length[list]}];
graphlist = Table[Plot[{h[x], linelist[[point]]}, {x, -10, 10}], {point, 1, Length[linelist]}];
Manipulate[ Show[graphlist[[a]], pointlist[[a]]], {a, 1, Length[graphlist] - 1, 1}]
```

Just set your H[x] and your starting point and you are good to go!