The number of integral values of a in `[0,10)` so that function, `f(x)=x^(3)-3(7-a)x^(2)-3(9-a^(2))x+2017` assume local minimum value at some `xepsilonR^(-)`

Explanation

To solve the problem, we need to determine the number of integral values of \( a \) in the interval \([0, 10)\) such that the function

\[ f(x) = x^3 - 3(7-a)x^2 - 3(9-a^2)x + 2017 \]

assumes a local minimum at some \( x \in \mathbb{R} \).

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