Is $f(x)=\frac{x^2-7x12}{x-3}$ differentiable at $x=3?$ Justify your answer.

Choose the correct answer below.

A$.$ Yes, the function is differentiable because $f(x)$ is not continuous at $x=3.$

B$.$ No$,$ the function is not differentiable because $f^{\text{'}}(x)=0$ at $x=3.$

C$.$ No$,$ the function is not differentiable because $f(x)$ is not continuous at $x=3.$

D$.$ Yes the function is differentiable because $f(x)$ is continuous at $x=3.$