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Working on my AP Calc summer assignment and I am having a hard time understanding how to solve this; I could really use some very dumbed-down help if possible because I don't even know where to start. Here it is...

Determine where the function is continuous and where the function is differentiable.

$$f(x)=\begin{cases}(x+1)^2,& x \leq 0\\ 2x+1,& 0< x < 3\\ (4-x)^2,& x \geq 3\end{cases}$$

Thank you in advance for your help!

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    Hint: Is it already clear to you that the function is continuous and differentiable everywhere except possibly 0 and 3, and you simply need to find which properties it fulfills at 0 and 3?2011-08-23
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    That makes sense but how would I go about doing that? I've never worked with piecewise functions before.2011-08-23

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