If the function `f(x)=x^3-9k\ x^2+27 x+30` is increasing on `R` , then (a) `-1lt=k<1` (b) `k<-1` or `k >1` (c) `0

Explanation

To determine the condition for which the function \( f(x) = x^3 - 9kx^2 + 27x + 30 \) is increasing on \( \mathbb{R} \), we need to analyze the first derivative \( f'(x) \).

### Step 1: Find the first derivative of the function
The first derivative of the function \( f(x) \) is given by:
\[ f'(x) = \frac{d}{dx}(x^3 - 9kx^2 + 27x + 30) \]
Calculating this, we get:
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