Newton’s Method
Whenfacedwith a mathematicalproblemthat cannotbe solvedwith simplealgebraicmeans,suchas
findingthe rootsof the polynomial calculussometimesprovidesa way of findingthe
approximatesolutions.
Let'ssay we are interestedin computing withoutusinga calculatoror a table.To do so, thinkabout
this problemin a differentway. Assumethat we are interestedin solvingthe quadraticequation
whichleadsto the roots.
The idea here is to find the linearizationof the abovefunction,whichis a straight-lineequation,and then
solvethe linearequationforx.
Since
or
We choosethe linearapproximationoff(x) to be nearx 0 = 2. Since and thus
and Usingthe linearapproximationformula,