An ideal calculus problem

Calculus Level 5

If the function

\(\large{f(x)=2x^{3}-(8-a)x^{2}+(a^{2}+\frac{19}{6})x-12}\)

has a local minima at some \(x\in R^{-}\) then value of \(a\) where \(a\in R\)

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