It would help pitch answers at the correct level ifOriginally Posted by mr_pj
you tell us what course/level you are studying.
Look at the definition of , it is the
difference of two positive functions of :
is zero when these two functions are
equal. Now is an increasing function and
is a decreasing function of .
So it they are equal at some point, this is the only point at
which they are ever equal. This is clear if you sketch the
two functions (see attachment).
Look at your notes to find what the Newton's Method
is. You will find it gives you a new estimate of the
root of a function in terms of the old estimate.
You start with a guess, get a new estimate and feed
that back, repeating the procedure until it has converged
sufficiently for your purposes.
In this case starting with a guess of 2 I get: