I've been asked to finding the roots of the equation $x^3-6x+2=0$. They've called it the 'pivot method' but I can't seem to find the 'real' name of it. I've looked at secant, newton, bisection etc... and nothing seems to match this. The method is as follows:
To solve $f(x)=0$, select $2$ $x$'s values between which the exact solution lies, say $x=a$ and $x=b$. Draw vertical lines through $x=a$ and $x=b$ to meet $f(x)$ at $P$ and $Q$. The point where $\overline{PQ}$ cuts the $x$ axis appears to be a better approximation to the exact solution than either $x=a$ and $x=b$. consider this new point $x=c$. Then basically this repeats and a vertical is drawn at $x=c$ to meet the curve and then it gets connected to the top point and where that cuts the $x$ axis is a better approximation again.
If anyone knows what this method is called or understands it please help! Thanks
Looks like the False Position method: https://en.wikipedia.org/wiki/False_position_method ?