$\mathrm{f}\left(\mathrm{x}\right)=\left\{\begin{array}{cc}4\mathrm{x}-{\mathrm{x}}^3+ln\left({\mathrm{a}}^2-3\mathrm{a}+3\right),& 0\le \mathrm{x}<3\\ \mathrm{x}-18& \mathrm{x}\ge 3\end{array}\right.$Complete set of values of a such that f(x) has a local minima at x = 3 is

Clearly, f(x) in decreasing just before x = 3 and increasing after x = 3. For x = 3 be the point
Of local minima, f (3) $\le$ (3^-).
or -15 $\le$ 12 - 27 + in(a² - 3a + 3)
or a² - 3a + 3 $\ge$ 1
or a $\notin$(-$\infty$,1)$\cup$(2,$\infty$).