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If f:R rarr R is a twice differentiable ...

If `f:R rarr R` is a twice differentiable function such `f(x)gt` for all x `in R and f(1/2)=1/2,f(1)=1`, then

A

`f'(1)le0`

B

`f'(1)gt1`

C

`0ltf'(1)le(1)/(2)`

D

`(1)/(2) ltf'(1) le1`

Text Solution

Verified by Experts

The correct Answer is:
B
f'(x) is increasing
For some x in `((1)/(2),1)`
`f'(x)=1" "[ LMVT]`
`:. f'(1)gr=1`
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