Problem:
Use the bisection method to find a root of the function

f(x) = x3 - 7 x - 4.


Visualization:
Using Microcalc:

  1. Choose Intermediate Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Bisection, press and .
  3. At the prompt F(x) =, enter the function
    x^3 - 7x - 4
  4. and use the bounds
    x0 = 0 x1 = 3
  5. Use the arrow keys to move to Automatic Bisect. and press . You will see the following table:

     m = Midpoint of [x0, x1]
    +-------------------------------------------------------------------+
                x0 m = (x0 + x1)             x1   F(x0)   F(m)  F(x1) 
    -------------------------------------------------------------------
       0.00000 000    1.50000 000    3.00000 000     < 0    < 0    > 0 
       1.50000 000    2.25000 000    3.00000 000     < 0    < 0    > 0 
       2.25000 000    2.62500 000    3.00000 000     < 0    < 0    > 0 
       2.62500 000    2.81250 000    3.00000 000     < 0    < 0    > 0 
       2.81250 000    2.90625 000    3.00000 000     < 0    > 0    > 0 
                                                                       
       2.81250 000    2.85937 500    2.90625 000     < 0    < 0    > 0 
       2.85937 500    2.88281 250    2.90625 000     < 0    < 0    > 0 
       2.88281 250    2.89453 125    2.90625 000     < 0    < 0    > 0 
       2.89453 125    2.90039 063    2.90625 000     < 0    > 0    > 0 
       2.89453 125    2.89746 094    2.90039 063     < 0    > 0    > 0 
    +-------------------------------------------------------------------+
    

  6. If you want greater accuracy, use the arrow keys to move to Automatic Bisect. and press .