## Calculus: Early Transcendentals (2nd Edition)

It is not differentiable at $x=2$.
The given function is a rational function and it has $x-2$ in the denominator. Since the denominator has to be different than zero we see that $x-2\neq0$ which is for $x\neq2$ and this says that $x=2$ is not in the domain of the function. Every point at which the derivative is defined (i.e. where the function is differentiable) must be in the domain. Because $x=2$ is not, the function is not differentiable at $x=2$.