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Problem 72 Hard Difficulty

At what numbers is the following function $ g $ differentiable?
$ g(x) = \left\{
\begin{array}{ll}
2x & \mbox{if}x \le 0\\
2x - x^2 & \mbox{if}0 < x < 2\\
2 - x & \mbox{if}x \ge 2
\end{array} \right. $
Give a formula for $ g' $ and sketch the graphs of $ g $ and $ g'. $

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Video Transcript

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