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Calculus Level 4

Given that,

\[\large f(x) = \color{blue}{\text{max}} \begin{cases} \text{sgn}(x) \\ x^3 \\ -\sqrt{9 - x^2} \hspace{.3cm} \small\text{ where defined} \\ -x^2 \end{cases} \]

The number of points where the function \(f(x)\) is not differentiable for \( x\in\Bbb R\) are ....?


Bonus:

  • Draw the graph for quick solution.
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