To find the interval where the function $f(x) = 3x^2 - 6x + 2$ is decreasing, we need to follow these steps:

1. Find the derivative $f'(x)$: The first derivative of the function will give us the rate of change of $f(x)$ with respect to $x$. The function is decreasing where this derivative is negative.

   $f'(x) = \frac{d}{dx} \left( 3x^2 - 6x + 2 \right)$

   $f'(x) = 6x - 6$

2. Determine where $f'(x) < 0$: The function is decreasing where the derivative is less than zero.

   $6x - 6 < 0$

   $6x < 6$

   $x < 1$

Thus, the function $f(x) = 3x^2 - 6x + 2$ is decreasing on the interval $(-\infty, 1)$.

Would you like any further details or have any questions?

Here are some related questions you might consider:

1. What is the interval where the function is increasing?
2. How do you find the critical points of a function?
3. What is the second derivative of $f(x)$ and what does it indicate?
4. How do you determine the local minimum and maximum points of a function?
5. How can you find the vertex of the quadratic function $f(x) = 3x^2 - 6x + 2$?

Tip: When analyzing the behavior of functions, always start by finding the derivative. The sign of the derivative helps determine if the function is increasing or decreasing.