Consider the function $f(x)$ defined by

$f(x)=\{\begin{array}{cc}3x^2-5ax+3b,& x<mn>2</mn>\\ 2a{x}^3-3xb+5,& 2x\end{array}$

For which values of a and b$,$ if any, is $f(x)$ continuous at $x=2?$

Choose all the correct answers below:

$a=-\frac{1}{2},b=-\frac{20}{9}$

$a=-\frac{2}{3},b=\frac{5}{9}$

$a=\frac{1}{3},b=1$

$a=\frac{3}{2},b=\frac{32}{9}$

None of the given answers.

$a=\frac{2}{3},b=\frac{31}{27}$