Find the intervals in which the function `f(x)=x^3-12x^2+36x+17` is (a) increasing, (b) decreasing.

Explanation

To find the intervals in which the function \( f(x) = x^3 - 12x^2 + 36x + 17 \) is increasing or decreasing, we will follow these steps:

### Step 1: Differentiate the function
To determine where the function is increasing or decreasing, we first need to find its derivative.

\[ f'(x) = \frac{d}{dx}(x^3 - 12x^2 + 36x + 17) \]
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