Raiz nos métodos de Newton e Secante

// Raiz nos métodos de Newton e Secante
#include <cmath>
#include <cstdio>
#include <locale>

 double funcao( double x)
{
//    return pow( x, 3) - 9 * x + 3;
//    return pow( x + 1, 2) * pow( EULER, pow( x, 2) - 2) - 1;
    return 1000 * pow( x, 5) - 3 * x + 9.04;
}

 double derivada( double x)
{
//    return 3 * pow( x, 2) - 9;
//    return 2 * ( x + 1 ) * pow( EULER, pow( x, 2) - 2) +
//           2 * x * pow( x + 1, 2) * pow( EULER, pow( x, 2) - 2);
    return 5000 * pow( x, 4) - 3;
}

double newton( double xk)
{
    double xk_1;
    int iteracoes = 0;

    xk_1 = 0;
    while( true )
    {
        xk_1 = xk - ( funcao( xk) / derivada( xk) );
        iteracoes ++;
        if( std::abs( ( xk_1 - xk ) / xk_1 ) < 0.0000000001 ) break;
        xk = xk_1;
    }
    printf( "iterações : %i\n", iteracoes );
    return ( xk + xk_1) / 2;
}

double secante( double xk_1, double xk)
{
    double fxk, fxk_1, temp;
    int iteracoes = 0;

    while( true )
    {
        fxk = funcao( xk);
        fxk_1 = funcao( xk_1);
        temp = xk - ( fxk / ( ( fxk - fxk_1) / ( xk - xk_1) ) );
        iteracoes ++;
        if( std::abs( ( temp - xk ) / temp ) < 0.0000000001 ) break;
        xk_1 = xk;
        xk = temp;
    }
    printf( "iterações : %i\n", iteracoes );
    return ( temp + xk ) / 2;
}


int main( void)
{
    double x1, x2;
    int i;

    setlocale( LC_ALL, "");

    x1 = funcao( -3);
    printf( "%i : %2.17f\n", -3, x1 );
    for( i = -2; i <= 3; i++)
    {
        x2 = funcao( i);
        printf( "%i : %2.17f\n", i, x2 );
        if( ( x1 * x2) < 0 )
        {
            printf( "Newton : %2.17f\n", newton( i-0.5 ));
            printf( "Secante: %2.17f\n", secante( i-2, i-1) );
        }
        x1 = x2;
    }
    return 0;
}