(x^3+e^2x+5)^(1/3) It just ends up oscillating between 0.854 & -2.884
It is interesting to observe that the search of the solution of the equation with the Newton-Raphson method conducts to the difference equation...
... where is the function described in my previous post. At first it seems that nothing changes but it isn't!... The function is illustrated here...
The 'attractive fixed point' is [of course...] again at but [taht is the difference...] around is [the 'red line' in figure...] and that means that the sequence obtained from (1) will never converge to ...
When you pick an initial approximation to the root,
calculate the slope of the tangent,
find your next approximation and continue with the iterations,
your "next approximation" keeps going either side of the root.
There is one value of x that would cause you to "land on" the root.
But that would be pure luck!!