Pract: Develop a C program to compute derivatives of a tabulated function at a specified value using the Newton interpolation approach. (Newton’s Divided Interpolation Formula)

#include<stdio.h>
#include<conio.h>
#include<math.h>
void main()
{
float x[10],y[10][10],sum,p,u,temp;
int i,n,j,k=0,f,m;
float fact(int);
clrscr();
printf(“Enter total number of values: “);
scanf(“%d”,&n);
for(i=0; i<n; i++)
{
printf(“enter the value of x[%d]: “,i+1);
scanf(“%f”,&x[i]);
printf(“enter the value of y[%d]: “,i+1);
scanf(“%f”,&y[k][i]);
}
printf(“\nEnter X for finding y(x): “);
scanf(“%f”,&p);

for(i=1;i<n;i++)
{
k=i;
for(j=0;j<n-i;j++)
{
y[i][j]=(y[i-1][j+1]-y[i-1][j])/(x[k]-x[j]);
k++;
}
}
printf(“\n_____________________________________________________”);
printf(“\n  x(i)\t   y(i)\t    y1(i)    y2(i)    y3(i)    y4(i)”);
printf(“\n_____________________________________________________\n”);
for(i=0;i<n;i++)
{
printf(“\n %.3f”,x[i]);
for(j=0;j<n-i;j++)
{
printf(”   “);
printf(” %.3f”,y[j][i]);
}
printf(“\n”);
}

i=0;
do
{
if(x[i]<p && p<x[i+1])
k=1;
else
i++;
}while(k != 1);
f=i;

sum=0;
for(i=0;i<n-1;i++)
{
k=f;
temp=1;
for(j=0;j<i;j++)
{
temp = temp * (p – x[k]);
k++;
}
sum = sum + temp*(y[i][f]);
}
printf(“\n f(%.2f) = %f”,p,sum);
getch();
}