Apply Newton-Raphson method to find the solutions to Apply Newton-Raphson method to find the solutions to the equation $x^3-5x=0$ starting with an initial guess of $x_0 = 1$.
While using Newton Raphson method, the value doesn't converge to a specific number. Rather, every iteration either gives $1$ or $-1$. Why does this happen? Any graphical interpretation for this?

For the graph of $f(x)=x^3-5x$, we have $f'(x)=3x^2-5$
$$f(1)=-4$$
$$f'(-1)=4$$
$$f'(1)=-2=f'(-1)$$
The tangent line at $x=1$ is $y+4=-2(x-1)$ which is $y=-2x-2$.
The tangent line at $x=-1$ is $y-4=-2(x+1)$ which is $y=-2x+2$
Geometrically, what has happened is you are trapped in the following cycle.

Starting from $(1,-4)$, by traveling along the tangent, we intercept the $x$-axis at $x=-1$. From $(-1,4)$, by trveling along the tangent, we intercept the $x$-axis at $x=1$.
