If graph of the function f(x) =`3x^(4)+2x^(3)+ax^(2)-x+2` is concave upward for all real x, then find values of a,

Explanation

To determine the values of \( a \) for which the function \( f(x) = 3x^4 + 2x^3 + ax^2 - x + 2 \) is concave upward for all real \( x \), we follow these steps:

### Step 1: Find the first derivative \( f'(x) \)
The first derivative of the function \( f(x) \) is calculated as follows:
\[ f'(x) = \frac{d}{dx}(3x^4 + 2x^3 + ax^2 - x + 2) = 12x^3 + 6x^2 + 2ax - 1 \]

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