Iteration for solving $x=g(x)$.
$g(x) = \frac{x^2}{3}$
$P=3$
$p_0 = 3.5$
1) Graph $g(x)$, the line $y=x$, and the fixed point $P$ ( **done** )
2) Using the given starting value $p_0$, compute $p_1$ and $p_2$ ( **the answer might be** $p_1 = 4.083333,p_2 = 5.537869$)
Determine geometrically if fixed point iteration converges ( **answer: diverges** )
We might decide this using the analogical graphing structure:
!enter image description here
Please, help!
Writing $g(x)=x\cdot \frac{x}{3}$, we see that if $x>3$ then $g(x)>x$ and if $0\leq x<3$, then $g(x)