For g(x) = (x^3-1)/3, then g'(x) = x^2 By theory of convergence, |g'(x)| 1 which doesn't satisfy the therory of convergence. But why does g(1.8) converges to a value while theory of convergence is not...

For g(x) = (x^3-1)/3,

then g'(x) = x^2

By theory of convergence, |g'(x)|<1 means="" g(x)="" will="" converge="" to="" a="">

g'(1.8) = (1.8)^2 = 3.24 > 1 which doesn't satisfy the therory of convergence.

But why does g(1.8) converges to a value while theory of convergence is not satisfied?