I have the following function:
$$y = \begin{cases} x^3, &\text{if } x \lt 1, \\ 3x-2, &\text{if } x \geq 1. \end{cases}$$
It is a function where I get a transition at $x=1$... I am supposed to check whether the function is continuous/differentiable at that transition point... the problem is I don't really see how to do it. I graphed the thing, but once I try finding whether a tangent line exists at $x=1$, I have problems... Could anyone, please, give me a hint on where I should go?