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Let f:[2,4] to RR be a differentaible fu...

Let `f:[2,4] to RR` be a differentaible function such that
`(xlog_e x) f'(x)+(log_e x)f(x) +f(x) ge 1 , x in [2,4]` with `f(2)=1/2` and `f(4)=1/4`
Consider the following two statements :
(A): `f(x) le 1`, for all `x in [2,4]`
(B): `f(x) ge 1/8` , for all `x in [2,4]`
then

A

Only statement (B) is true

B

Only statement (A) is true

C

Both the statements (A) and (B) are true

D

Neither statements (A) nor statement (B) is true

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