If f(x)=logex is defined in [1,e], then...

If `f(x)=log_ex` is defined in [1,e], then

A

f(x) is an increasing function in (1,e)

B

f(x) holds Rolle's theorem and `c=1/e`

C

f(x) holds Lagrange's MVT and `f'(c)=1/(e-1)`

D

area enclosed by y=f(x) and the line passing through (1,0) and (e,1) is `(3-e)/2` sq. units

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The correct Answer is:

A, C, D

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