Raízes de pow( x + 1, 2) * pow( EULER, pow( x, 2) - 2) - 1;

// Raízes nos métodos de bisseção e Newton com margem de erro de 10 na -10
#include <cmath>
#include <cstdio>
#include <locale>

const double EULER = 2.718281828459045235360287;

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

 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);
}

 double bissecao( double a,  double b)
{
    double xk, xk_1;

    xk_1 = 0;
    while( true )
    {
        xk = ( a + b) / 2;
        if( ( funcao( a) * funcao( xk) ) < 0 )
        {
            b = xk;
        }
        else
        {
            a = xk;
        }
        if( std::abs( ( xk - xk_1 ) / xk ) < 0.0000000001 ) break;
        xk_1 = xk;
    }
    return ( a + b) / 2;
}

double newton( double xk)
{
    double xk_1;

    xk_1 = 0;
    while( true )
    {
        xk_1 = xk - ( funcao( xk) / derivada( xk) );
        if( std::abs( ( xk_1 - xk ) / xk_1 ) < 0.0000000001 ) break;
        xk = xk_1;
    }
    return ( xk + xk_1) / 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( "Bisseção: %2.17f\n", bissecao( i-1, i) );
            printf( "Newton :  %2.17f\n", newton( i-0.5 ));
        }
        x1 = x2;
    }
    return 0;
}