In order to find roots for f(x) = x*x*x - x*x- 9.0*x + 8.9 in theinterval -1.0 <

Question

In order to find roots for f(x) = x*x*x - x*x- 9.0*x + 8.9 in theinterval
-1.0 <= x <= 5.0, create a table for x and f(x) fromx=-1.0 to x=5.0 with
an increment of del_x=0.25. Mark the intervals with 'Y' where f(x)changes
sign. In the table, use %8.2f and %12.4f for printing values of xand
f(x).
In each interval where f(x) changes sign, use the mid-point valueof x as
an initial guess x0 for the Newton-Raphson method, obtain refinedroots
and print each root with %-12.6e. Use double Newton_Raphson(doublex0)
that gives a refined root for an initial guess of x0. (You are notallowed
to modify double Newton_Raphson().)

You need to write the following functions:
double func1(double x)   for f(x) = x*x*x - x*x-9.0*x + 8.9;
double func1_d(double x) for f'(x) = 3.0*x*x - 2.0*x - 9.0;
.......................................................................
Your output should look like this:

     x        f(x)     sign change
-----------------------------------------
   -1.00      15.9000
   -0.75      14.6656
   -0.50      13.0250
   -0.25      11.0719
    0.00      8.9000
    0.25      6.6031
    0.50      4.2750
    0.75      2.0094
    1.00     -0.1000    Y
     f(0.875) = 9.292969e-01
     f(0.984935) = 2.096803e-02
     f(0.987537) = 1.324866e-05
     f(0.987539) = 5.316636e-12
     A refined root is 9.875386e-01
    1.25      -1.9594
    1.50      -3.4750
    1.75      -4.5531
    ....      .......

Explanation / Answer

In order to find roots for f(x) = x*x*x - x*x- 9.0*x + 8.9 in theinterval -1.0

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