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Let f (x) = x^3-x^2-x+1 and g(x) = {max{...

Let `f (x) = x^3-x^2-x+1` and `g(x) = {max{f(t); 0<=t<=x}, 0<=x<=1, 3-x, 1<=x<=2` Discuss the continuity and differentiability of the function g (x) in the interval (0, 2).

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