Continuity and Differentiability of Max/Min

Rarely Tested
For $$f(x) = \max\{g(x), h(x)\}$$ or $$\min\{g(x), h(x)\}$$:
  • Continuous if $$g, h$$ continuous
  • Differentiable at $$c$$ (where $$g(c)=h(c)$$) iff $$g'(c) = h'(c)$$
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