A beautiful function

Calculus Level 4

For all $x$, we define the functions $f(x) = x^2$ , $g(x) = -x^2+1$, $p(x) = |x| + 1$. Consider the piecewise function $h(x)$,

$h(x) = \begin{cases} \max(f(x), g(x), p(x)) \quad,\quad x\geq -\dfrac{81}{100} \\ \min(f(x), g(x), p(x)) \quad,\quad x< -\dfrac{81}{100} \\ \end{cases}$

If $h(x)$ is non-diffentiable at $A$ points and non-continuous at $B$ points, find the value of $A+2B$.

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