A beautiful function

Calculus Level 4

For all xx, we define the functions f(x)=x2f(x) = x^2 , g(x)=x2+1 g(x) = -x^2+1, p(x)=x+1p(x) = |x| + 1 . Consider the piecewise function h(x)h(x) ,

h(x)={max(f(x),g(x),p(x)),x81100min(f(x),g(x),p(x)),x<81100 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)h(x) is non-diffentiable at AA points and non-continuous at BB points, find the value of A+2BA+2B.

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