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4.4.4  fsolve or nSolve with the option newton_solver

newton_solver is the standard Newton method. The algorithm starts at an init value x0, then we search the intersection x1 of the tangent at x0 to the graph of f, with the x axis, the next iteration is done with x1 instead of x0. The xi sequence is defined by

x0=x0,    xn+1=xn
f(xn)
f′(xn)
 

If the Newton method converges, it is a quadratic convergence for roots of multiplicity 1.
Input :

fsolve((cos(x))=x,x,0,newton_solver)

Output :

0.739085133215

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