Find the intervals in which the function `f` given by `f(x)=\ x^3+1/(x^3)\ ,\ x\ !=0\ \ ` is (i) increasing (ii) decreasing.

Explanation

To determine the intervals in which the function \( f(x) = x^3 + \frac{1}{x^3} \) (for \( x \neq 0 \)) is increasing or decreasing, we will follow these steps:

### Step 1: Find the derivative of the function
We start by differentiating the function \( f(x) \).

\[ f'(x) = \frac{d}{dx} \left( x^3 + \frac{1}{x^3} \right) \]
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