// ------------------------------------------------------
// newton-method
// 
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
// ------------------------------------------------------
double A, B, C, M, N;
double func(double x)
{
	// func(x) = A*e^(m*t)+B*e^(n*t) - C
	return 
		A * exp(M*x) + B * exp(N*x) - C;
}
 
double funcd(double x)
{
	// funcd(x) = func'(x)
	// funcd(x) = A*m*e^(m*t)+B*n*e^(n*t)
	return 
		A * M * exp(M*x) + B * N * exp(N*x) - C;
}
 
// -------------------------------------------------------
double NewtonRoot(double x0,/*   初點  */
	double (*fx)(double),   /* 適應函式*/
	double (*fd)(double),   /* 微分函式*/
	double eps,             /* 容許誤差*/
	int max_itera)          /* 最大迭代*/
{
	double x=x0;
	do{
		x0=x;
		x = x0 - fx(x0) / fd(x0);
	}while(fabs(x-x0)>eps && max_itera--);
	return x;
}
 
// -------------------------------------------------------
int main()
{
	const double eps=1E-15;
	const int max_iterator=1000000;
	double x0, x;
 
	puts("A * e^(mx) + B * e^(nx) - C = 0 < newton method >");
	printf("input A : "); scanf("%lf", &A);
	printf("input B : "); scanf("%lf", &B);
	printf("input C : "); scanf("%lf", &C);
	printf("input N : "); scanf("%lf", &N);
	printf("input M : "); scanf("%lf", &M);
	printf("input x0: "); scanf("%lf", &x0);
 
	x = NewtonRoot(x0, func, funcd, eps, max_iterator);
 
	puts("");
	printf("x       : %.15lf\n", x);
	printf("func(x) : %.15lf\n", func(x));
	// system("pause"); // 看不到結果加入這行
	return 0;
}

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

MS4yMzQKMy4xNDUKMTAwLjE0NQozLjMzNwo2LjE0NQo1CgoxMDAwLjI0NwoxMjMuNTk3CjEyMzQ3LjM0NQotMTAuMgotNS43Ci03LjgKCjEKMgo0CjgKMTYKMA==

1.234
3.145
100.145
3.337
6.145
5

1000.247
123.597
12347.345
-10.2
-5.7
-7.8

1
2
4
8
16
0