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Consider the function f:(0,2)rarr R defi...

Consider the function `f:(0,2)rarr R` defined by `f(x)=(x)/(2)+(2)/(x)` and the function `g(x)` defined by
`g(x)={(min f(t) , 0 lt t le x, 0 lt x le1),``((3)/(2)+x,1 lt x lt 2):}` .Then

A

"g" is continuous and differentiable for all `x in(0,2)`

B

"g" is continuous but not differentiable at "x=1

C

"g" is not continuous for all "x in(0,2)

D

"g" is neither continuous nor differentiable at "x=1

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