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F(x) =x^3-3x^2+6 and g(x)= max{F(t):x+1...

`F(x) =x^3-3x^2+6` and `g(x)= max{F(t):x+1<=t<=x+2} -3<=x<0` and `1-x` for `x>=0` Find continuity and differentiability of g(x) for `x in [-3,1]`

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