Question

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`?

Answer 1

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;

`Delta = b^2-4ac = 9-24 lt 0`

Therefore `f(x)=0` has no (real) solution and therefore an iterative approach will fail.