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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) 0letlex 0lexle1),(3-x 1ltxle2):}` then

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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