Suppose that the piecewise defined function $f$ is defined by

$f(x)=\{\begin{array}{cc}1-2x,& x2\\ -3x^2+10x-11,& x>2\end{array}$

Determine which of the following statements are true.

Select the correct answer below:

$f$ is neither differentiable nor continuous at $x=2.$

$f$ is continuous but not differentiable at $x=2.$

$f$ is both differentiable and continuous at $x=2.$