Newton's Method

Each guess is a better approximation to the root of the equation than the previous guess. The process can be continued indefinately.

x_1

f(x_1)

Show Tangent to curve

x_2

Show First Guess

Show f(First Guess)

Show Second Guess

f(x_2)

Show f(Second Guess)

Show new Tangent

x_3

Show Third Guess

First Guess

f(x) = x^2 - 5

o = 1.1 (slider from 0.1 to 2, step 0.1)
f(x) = x^(2) - 5
A: (o, 0)
b = OrthogonalLine(A, xAxis)
B = Intersect(f, b)
c = Segment(A, B)
e = Tangent(B, f)
g = false
C = Intersect(e, xAxis)
T4: "x_1 = " + (x(A))
a = true
T5: "f(x_1)  =" + (y(B))
d = false
T6: "x_2 = " + (x(C))
h = false
i = OrthogonalLine(C, xAxis)
D = Intersect(f, i)
j = Segment(C, D)
T8: "f(x_2) = " + (y(D))
k = false
l = Tangent(D, f)
m = false
E = Intersect(l, xAxis)
T9: "x_3 = " + (x(E))
n = false