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Let f: [0, 8]to R be differentiable func...

Let `f: [0, 8]to R` be differentiable function such that `f (0) =0, f (4)=1, f (8) =1,` then which of the following hold(s) good ?

A

There exist some `c _(1) in (0,8)` where `f (c _(1)) =1/4 `

B

There exist some `x in (0,8)` where `f '(c ) =1/12`

C

There exist `c _(1), c _(2) in [0,8]` where `8f ' (c _(1)) f (c _(2)) =1`

D

There exist some `alpha, beta=(0,2)` such that `int _(0)^(8)f(t) dt =3 ( alpha ^(2) f (alpha ^(3)) + beta ^(2) (beta ^(3)))`

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The correct Answer is:
A, C, D
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VK JAISWAL ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (ONE OR MORE THAN ANSWER IS/ARE CORRECT )
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