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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

discontinuous at only one point

B

continuous at `x=0`

C

discontinuous at `x=2`

D

continuous everywhere in (0,2)

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`g(x)={{:(x^(2)-x^(2)|x+1,0lexle1),(3-x,1lt2):}` as f(x) is increasing
function
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