Find the intervals in which the function f(x) = `2x^(3)-15x^(2)+36x + 6` is (i) increasing, (ii) decreasing.

Explanation

To find the intervals in which the function \( f(x) = 2x^3 - 15x^2 + 36x + 6 \) is increasing or decreasing, we will follow these steps:

### Step 1: Find the derivative of the function
To determine where the function is increasing or decreasing, we first need to find the derivative \( f'(x) \).

\[ f'(x) = \frac{d}{dx}(2x^3 - 15x^2 + 36x + 6) \]
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