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Let f be a non-negative function defined...

Let `f` be a non-negative function defined on the interval `[0,1]dot` If `int_0^xsqrt(1-(f^(prime)(t))^2)dt=int_0^xf(t)dt ,0lt=xlt=1,a n df(0)=0,t h e n` `f(1/2)<<1/2a n df(1/3)>>1/3` `f(1/2)>1/2a n df(1/3)>1/3` `f(1/2)<1/2a n df(1/3)<1/3` `f(1/2)>1/2a n df(1/3)<1/3`

A

`f(1/2)lt 1/2` and `f(1/3)gt1/3`

B

`f(1/2)gt 1/2` and `f(1/3)gt1/3`

C

`f(1/2)lt 1/2` and `f(1/3)lt1/3`

D

`f(1/2)gt 1/2` and `f(1/3)lt1/3`

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