The equation f(x) = g(x) has an approximate solution of 7, found using successive approximations with initial guess 5/8.
The image shows a table of successive approximations for the solution to the equation f(x) = g(x), where f(x) = x^3 - 3x^2 - x - 6 and g(x) = x^2 - 3x - 2. The table shows the intersection values of the graphs of f(x) and g(x) starting with the initial guess x = 5/8.
To use successive approximations, we start with an initial guess and then iteratively compute the following:
x_{n+1} = f(x_n)
This means that the next guess is the output of the function at the previous guess. We continue this process until the difference between two successive guesses is below a certain threshold.
The table in the image shows the results of successive approximations for the equation f(x) = g(x). We can see that the intersection value of the graphs is approximately 7. This is because the two successive guesses 15/16 and 7/8 are very close to each other.