If the Rolle's theorem is applicable to ...

If the Rolle's theorem is applicable to the function f defined by
`f(x)={{:(ax^(2)+b",", |x|le1),(1",", |x|=1),((c)/(|x|)",",|x|gt1):}`
in the interval `[-3, 3]`, then which of the following alternative(s) is/are correct?

A

A) `a+b+c=2`

B

B) `|a|+|b|+|c|=3`

C

C) `2a+4b+3c=8`

D

D) `4a^(2)+4b^(2)+5c^(2)=15`

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The correct Answer is:

A, B, C, D

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