C programming:

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^2 + 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) = 2ax + b

The integral of the function f(x) (let us call it F(x)) indicates the area underneath the curve. Between points x _1 and x_2, the area A is

A = F(x_2) - F(x_1)

where, for a second-degree polynomial,

F(x) = (a/3)x^3 + (b/2)x^2 + cx

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_i), the final value of x (denote it x_f), and the increment value between successive x values (denote it deltaX).

Follow these detailed instructions:

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.

When you write your code, include the usual (detailed) comment block including program name, author, date, inputs, outputs and description.

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 main().

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_i, x_f and deltaX. Use double for all variables and calculations.

Your program is to loop over all possible x values in your main() function. The first x value is to be x_i , the second x_i + deltaX, etc. with the last value being x_f (or somewhat less than x_f if deltaX does not divide evenly into the range).

The calculation of the area A depends on the initial value of x, x_i. That is, for each x, we calculate the area as A = F(x) - F(x_i). In order to calculate A, you must know both x and x_i. For the first value of x, it should be that A is zero.

******** (This is the most important part please use comments to explain what you are doing) *****************

From main() and for each x, you are to call a function that accepts a, b, c, x and x_i. Calculate and return (via pointer operations) f (x), f ' (x) and A. That is, you must create a single function that accepts eight inputs five are call-by-value (a, b, c, x and x_i), and three are call-by-reference (pointers related to f(x), f ' (x) and A). There must not be any scan/print statements in your function.

Your function uses the values of a, b and c along with the value of x to compute f(x) = ax^2 + bx + c. Similarly, the derivative is computed as f ' (x) = 2ax + b. Then, using x_i in addition to the other parameters, compute F(x_i) = (a/3)x_i^3 + (b/2)x_i^2 + cx_i and F(x) = (a/3)x^3 + (b/2)x^2 + cx. The area is found as A = F(x) - F (x_i). Return the result of your calculations back to the main() function (it will be necessary to reference your outputs via pointers).

All output for your table of x versus f(x), f ' (x) and A must be displayed via statements in your main() function. Write your table to the terminal (i.e., the default output for printf()). Choose a suitable format for your output numbers.

An example of what the output table should look like is given below. Assume that the user enters 2.0 -2.0 -1.0 for a, b, c, respectively, and 0.0 5.0 0.25 for x_i, x_f and deltaX, respectively. Your output should be the following:

f(x) = 2x^2 + -2x + -1

x f(x) f'(x) A

-------------------------------

0.000 -1.000 -2.000 0.000

0.250 -1.375 -1.000 -0.302

0.500 -1.500 0.000 -0.667

0.750 -1.375 1.000 -1.031

1.000 -1.000 2.000 -1.333

1.250 -0.375 3.000 -1.510

1.500 0.500 4.000 -1.500

1.750 1.625 5.000 -1.240

2.000 3.000 6.000 -0.667

2.250 4.625 7.000 0.281

2.500 6.500 8.000 1.667

2.750 8.625 9.000 3.552

3.000 11.000 10.000 6.000

3.250 13.625 11.000 9.073

3.500 16.500 12.000 12.833

3.750 19.625 13.000 17.344

4.000 23.000 14.000 22.667

4.250 26.625 15.000 28.865

4.500 30.500 16.000 36.000

4.750 34.625 17.000 44.135

5.000 39.000 18.000 53.333

Use the test set as given above.