The utility of derivative

A major feature in calculus is “change”.
We require to know how a thing is changing another one so.. we could say “the relationship between two things is a function“. As we wiggle the input point of a function we can know how the output is changing.
But a question is still open What is the ratio which is changing the output value?
Well such ratio is the derivative.

slope_ecuation

#include <stdio.h>
#include <stdint.h>

#define __MAX_X_VALUE  20

static int f_x(int x)
{
   return 6*x - 9;
}

int main(void)
{
    for(int a = 0; a < __MAX_X_VALUE ;a++)
    {
       printf("f(%d)= 6(%d)-9 = %d\n", a, a, f_x(a));
    }
}
optimus@house:~$ g++ slope_ecuation.cpp ; ./a.out
f(0)= 6(0)-9 = -9
f(1)= 6(1)-9 = -3
f(2)= 6(2)-9 = 3
f(3)= 6(3)-9 = 9
f(4)= 6(4)-9 = 15
f(5)= 6(5)-9 = 21
f(6)= 6(6)-9 = 27
f(7)= 6(7)-9 = 33
f(8)= 6(8)-9 = 39
f(9)= 6(9)-9 = 45
f(10)= 6(10)-9 = 51
f(11)= 6(11)-9 = 57
f(12)= 6(12)-9 = 63
f(13)= 6(13)-9 = 69
f(14)= 6(14)-9 = 75
f(15)= 6(15)-9 = 81
f(16)= 6(16)-9 = 87
f(17)= 6(17)-9 = 93
f(18)= 6(18)-9 = 99
f(19)= 6(19)-9 = 105
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