double interpolate(int numberofpairs, double x[], double y[], double bigx, int k)
{
	int i=0,j=0,width=0;
	int upperbound=0,lowerbound = 0;
	double fx=0;



	for (i=0;i<numberofpairs;i++) 
	{
		if (x[i]>bigx)
		{
			lowerbound=i-1;
			upperbound=i;
			break;
		}
	}
	width = (k/2) - 1;
	upperbound+=width;
	lowerbound-=width;

	if (lowerbound < 0) 
	{
		upperbound = (abs(lowerbound)+upperbound);
		lowerbound = 0; 	
	}
	else 
	{

		if(upperbound > numberofpairs)  
		{
			lowerbound=lowerbound-(abs(upperbound-numberofpairs));
			upperbound=numberofpairs;
		}
	}

	fx = summation(x,y,numberofpairs,bigx,upperbound,lowerbound);
	//printf("fx is %lf\n", fx);
	return fx;
}