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Let F (x) = (f (x ))^(2) + (f' (x ))^(2)...

Let `F (x) = (f (x ))^(2) + (f' (x ))^(2), F (0) =6,` whtere f (x) is a thrice differentiable function such that `|f (x) || le 1 AA x in [-1, 1], ` then choose the correct statement (s)

A

There is atleast and point in each of the intervals `(-1, 0)` and (0, 1) where `|f'(x)|le 2`

B

There is atleast one point in each of the intervals `(-1, 0)` and 0, 1) where `F(x)le5`

C

There is no point of local maxima of F(x) in `(-1, 1)`

D

For some `c in (-1, 1), F(c)ge 6, F'(c) =0 and F''(c) le0`

Text Solution

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The correct Answer is:
A, B, D
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