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

Let `f(x) = x^(3) - x^(2) + x + 1 and`
`g(x) = {{:(max f(t)",", 0 le t le x,"for",0 le x le 1),(3-x",",1 lt x le 2,,):}` Then, g(x) in [0, 2] is
a. continuous for `x in [0, 2] - {1}`
b. continuous for `x in [0, 2]`
c. differentiable for all `x in [0, 2]`
d. differentiable for all `x in [0, 2] - {1}`

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