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

Let `f(x) = x^(3)- x^(2)+x+1and `
`g(x) ={{:(max.f(t) , 0le tle x, " for" o le x le 1),( 3-x, 1lt x le 2,):}`
Discuss the continuity and differentiability of g(x) in (0,2).

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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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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