Let f(x)`=x^(3) +3(a-7)x^(2)+3(a^(2) -9) x-1.` If f(x) has positive point of maxima then find possible values of 'a'

Explanation

To solve the problem, we need to find the values of \( a \) such that the function \( f(x) = x^3 + 3(a-7)x^2 + 3(a^2 - 9)x - 1 \) has a positive point of maxima. We will follow these steps:

### Step 1: Differentiate the function
We start by differentiating \( f(x) \) with respect to \( x \):

\[ f'(x) = \frac{d}{dx}(x^3) + \frac{d}{dx}(3(a-7)x^2) + \frac{d}{dx}(3(a^2 - 9)x) - \frac{d}{dx}(1) \]
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