Let f:[a,b]to[1,oo) be a continuous func...

Let `f:[a,b]to[1,oo)` be a continuous function and let `g:RtoR` be defined as
`g(x)={(0,"if",xlta),(int_(a)^(x)f(t)dt,"if",alexleb),(int_(a)^(b)f(t)dt,"if",xgtb):}` Then

A

g(x) is continuous but not differentibale at x

B

g(x) is differentiable on R

C

g(x) is continuous but not differentiable at b

D

g (x) is continuous and differentiable at either a or b but not both

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The correct Answer is:

A, C

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