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

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

A

g(x) is continuous but not differentiable at a

B

g(x) is differentiable on `RR`

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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