Given a function f(x) = x(9 - x).
We need to find the value of f(2) and f(2.1) and use them to approximate the value of f'(2).
The value of f(2) is calculated below:
The value of the f(2.1) is calculated as follows:
Now, by the definition of f'(x), we know that
For the given condition, x = 2, and delta x = 0.1. So, the value of f'(2) is
Thus, the approximate value of f'(2) is 4.9.