# 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