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

Let `f (x)= x^3+ x^2+ x+ 1` and `g(x)=max[f(t)] , 0<=t<=x , 0<=x<=1` and `f(x)=3-x , 1 < x<=2` then function `g(x)` 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`

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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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