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Let f : [a , b]rarr [1, infty] be a cont...

Let f : [a , b]`rarr [1, infty]` be a continuous function and let g : R `rarr` R be defined as
`g(x)={(0 if x lt a),(int_a^x f(t) dt if a le x le b),(int_a^b f(t) dt if x gt b):}`
Then

A

g(x) is continuous but not differentiable at a

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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