# Max, Min

Calculus Level 3

In the following functions, $$x$$ is any real number.

$\large f(x) = |x|+1 \\ \large g(x)=x^2+1$ Let $$h(x) = \begin{cases} \text{ max}\{ f(x), \ g(x) \} & \text{ if } x\le 0 \\ \text{ min}\{ f(x), \ g(x) \} & \text{ if } x>0 \end{cases}$$

Find the total number of points at which $$h(x)$$ is not differentiable.

Notation: $$| \cdot |$$ denotes the absolute value function.

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