/* -*-ePiX-*- */
#include "epix.h"
using namespace ePiX;

double f(double x)
{
  return -1 + x*(0.5 + 0.125*x + 0.005*pow(x, 6));
}

Deriv fp(f);

double df(double x)
{
  return fp.eval(x);
}

double iter(double x)
{
  return x - f(x)/df(x);
}

int main()
{
  picture(P(0,-1), P(2,1), "1.5 x 1.25in");

  begin();
  bold();

  double alpha(xmin()), beta(xmax()), T(iter(beta));

  P xA(alpha), xB(beta), pA(P(alpha, f(alpha))), pB(beta,  f(beta));

  line(xA, xB);

  line(xA, pA);
  line(xB, pB);
  line(P(T), pB);

  plot(f, alpha, beta, 40);

  dashed();
  line(pA, pB);

  label(xA, P(0,2),  "$\\alpha$", t);
  label(pA, P(-2,0), "$A$", l);

  label(xB, P(0,-2),  "$\\beta$", b);
  label(pB, P(2, 0), "$B$", r);

  label(P(T), P(0,-2), "$T$", b);
  label(Segment(pA, pB)*Segment(xA, xB), P(-2,2), "$c$", tl);

  label(P(0.5*xmax(), ymin()), P(0,-12), "\\textsc{Fig.~24}", b);

  tikz_format();

  end();
}