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

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

`g(x)` is discontinuous at `x=1`

B

`g(x)` is continuous at `x=1`

C

`g(x)` is differentiable at `x=1`

D

`g(x)` is non differentiable at `x=1`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`f(t)=t^(3)-t^(2)+t+1`
`f^(')(t)gt0`
`"max"f(t)0letlex=f(x)`
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