Find the values `' a '` for which the function `f(x)=(a+2)x^3-3a x^2+9a x-1` decreases for all real values of `x` .

Explanation

To find the values of \( a \) for which the function \( f(x) = (a+2)x^3 - 3ax^2 + 9ax - 1 \) is decreasing for all real values of \( x \), we need to analyze the first derivative of the function.

### Step 1: Find the first derivative \( f'(x) \)

The first derivative of the function \( f(x) \) is given by:

\[
f'(x) = \frac{d}{dx} \left( (a+2)x^3 - 3ax^2 + 9ax - 1 \right)
...