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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