Question

C-Programming please.

The task is to create second-degree polynomial calculator for the function, its integral and its derivative. A second-degree polynomial is described by the equation f(x) = ax +bx+c. Evaluation of the derivative gives the instantaneous slope or rate of change as (where f'(x) is the derivative of f(x)): f"(x)=2x+b The integral of the function f(x) (let us call it F(x)) indicates the area underneath the curve. Between points x; and the area A is A = F(x)-F(x), where, for a second-degree polynomial, F(x)= x + x +ex. Your program will be used to create a table of data of the independent variable x versus f(x), f(x) and A. The user will enter the polynomial coefficients {a,b,c} as well as the starting value of x (denote it x ), the final value of x (denote it x, ), and the increment value between successive x values (denote it Ax). Follow these detailed instructions: 1. First, read this document in its entirety. After reading this handout, you may optionally create a design sheet for the problem. Your design sheet should help you determine what header files, functions and variables you will need as well as identifying expected test results. You do NOT turn in your design sheet. 2. When you write your code include the usual (detailed) comment block including program name, author, date, inputs, outputs and description. 3. Create a function of type void to explain the program to the user with the description printed to the terminal. Do not forget to call the function from mainl). 4. Input the data while executing from your main!) function. Query the user to enter the data. You must enter the parameters from the user in the following order: a, b, c and then X, X, and Ar. Use double for all variables and calculations.

Answer 1

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define MAX_SIZE 100

void explain ();
double userinput(char*);
void calculations(int a, int b, int c, int x, int x_initial, double *f, double *fprime, double *area);

int main()
{
double a, b, c, xi, xf, deltaX; // a, b, c, x initial, x final and x step variables
double x[MAX_SIZE], f[MAX_SIZE], fprime[MAX_SIZE], A[MAX_SIZE];
int i = 0; //counter for for loops
int N = 0; // the size of the arrays
explain();

//prompts user to enter values
a = userinput("Enter a value for a:\n");
b = userinput("Enter a value for b:\n");
c = userinput("Enter a value for c:\n");
xi = userinput("Enter a value for x initial:\n");
xf = userinput("Enter a value for x final:\n");
deltaX = userinput("Enter a value for x step:\n");

printf("f(x) = %gx^2 + %gx + %g\n\n", a, b, c);

N = xf / deltaX; // the seize of all arrays

printf(" x\tf(x)\tf'(x)\tA\t\n");
printf("-----------------------------\n");

for(i = 0; i <= N; i++) {
x[i] = xi + (i * deltaX);
calculations(a, b, c, x[i], xi, &f[i], &fprime[i], &A[i]);
printf(" %.3f\t%.3f\t%.3f\t%.3f\t\n", x[i], f[i], fprime[i], A[i]);
}
return 0;

}

//explains the program to the user
void explain()
{
printf("Hello! This program accepts inputs for a, b, c, x initial,\n");
printf("x final and x step. The program generates and outputs f(x),\n");
printf("f'(x) and the area under the curve using the integral.\n\n");
}

//error checks for only numbers entering the program
double userinput(char message [])
{

double answer; //variable to hold answer
int status, error; //variable to check if there is an error

do
{
printf("%s", message);
status = scanf("%lf", &answer);

error = status != 1;

if (error)
{
printf("Input Error...\n");
fflush(stdin);
}
}
while (error);

return answer;
}

void calculations(int a, int b, int c, int x, int x_initial, double *f, double *fprime, double *area){
double Fx_i = 0;
double Fx = 0;

Fx_i = (a / 3) * (x_initial * x_initial * x_initial) + (b / 2) * (x_initial * x_initial) + c * x_initial;
Fx = (a / 3) * (x * x * x) + (b / 2) * (x * x) + c * x;

*f = (a * x * x) + (b * x) + c;
*fprime = (2 * a * x) + b;
*area = Fx - Fx_i;

}

Output: