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

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


Visualization:

Since f(0) < 0 and f(3) > 0, we use the bisection method on the closed interval [0,3] to obtain:

 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 
+-----------------------------------------------------------------------------+

This table was generated by Microcalc.


For this visualization, we have detailed instructions for the following software packages: