Determine the intervals in which the function `f(x)=x^4-8x^3+22 x^2-24 x+21` is decreasing or increasing.

Explanation

To determine the intervals in which the function \( f(x) = x^4 - 8x^3 + 22x^2 - 24x + 21 \) is increasing or decreasing, we will follow these steps:

### Step 1: Find the derivative of the function
To analyze the increasing and decreasing behavior of the function, we first need to find its derivative \( f'(x) \).

\[ f'(x) = \frac{d}{dx}(x^4 - 8x^3 + 22x^2 - 24x + 21) \]
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