Mathematics

Problem

Let

f : R \to R

and

g : R \to R

be respectively given by

f(x) = |x| + 1

and

g(x) = x^2 + 1

. Define

h : R \to R

h(x) = \begin{cases} \max\{f(x), g(x)\}, & \text{if } x \le 0. \\ \min\{f(x), g(x)\}, & \text{if } x > 0. \end{cases}

The number of points at which

h(x)

is not differentiable is