At the point $x=1$ the function $f(x)=\left\{\begin{array}{1 1}x^3-1&1 < x < \infty\\x-1&-\infty < x \leq 1\end{array}\right.$ is

Question

$\begin{array}{1 1}(a)\;\text{Continuous and differentiable}\\(b)\;\text{Continuous and not differentiable}\\(c)\;\text{DisContinuous and differentiable}\\(d)\;\text{DisContinuous and not differentiable}\end{array}$