How do you find the first three iterate of the function f(x)=3x^2−3x+2 for the given initial value x_0=1/3?

Jase Rocha

Jase Rocha

Answered question

2022-09-21

How do you find the first three iterate of the function f ( x ) = 3 x 2 - 3 x + 2 for the given initial value x 0 = 1 3 ?

Answer & Explanation

maceratorti

maceratorti

Beginner2022-09-22Added 10 answers

If we look at the graph of the function y=f(x):
graph{3x^2-3x+2 [-5, 5, -2, 5]}
We see that it is a quadratic that has no real roots. We can confirm this by looking at the discriminant;
Δ = b 2 - 4 a c = 9 - 24 < 0
Therefore f(x)=0 has no (real) solution and therefore an iterative approach will fail.

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