Minima and Least Value

Calculus Level 5

Let \[f\left( x \right) =\begin{cases} \left| { x }^{ 2 }-3x \right| +a\quad ;\quad 0\le x<\frac { 3 }{ 2 } \\ -2x+3\quad ;\quad x\ge \frac { 3 }{ 2 } \end{cases}\] If \(f\left( x \right)\) has a local \(maxima\) at \(x=\frac { 3 }{ 2 }\), then the \(least\) value of \(\left| 4a \right|\) is

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