Show that the function f(x)= ` x^(3) - 3x^(2)+3x - 1 ` is an increasing function on R.

Explanation

To show that the function \( f(x) = x^3 - 3x^2 + 3x - 1 \) is an increasing function on \( \mathbb{R} \), we need to demonstrate that its derivative \( f'(x) \) is greater than or equal to zero for all \( x \in \mathbb{R} \).

### Step 1: Find the derivative of the function

The first step is to compute the derivative \( f'(x) \).

\[
f(x) = x^3 - 3x^2 + 3x - 1
...