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For every twice differentiable function ...

For every twice differentiable function `f: R->[-2,\ 2]` with `(f(0))^2+(f^(prime)(0))^2=85`, which of the following statement(s) is (are) TRUE?

A

There exist r,s` in R`, where `r lt s` , such that f is one-one on the open interval (r,s)

B

There exist `x_(0) in (-4,0)` such that `|f'(x_(0))| le 1`

C

`lim_(x to oo) f(x)=1`

D

There exists `alpha in (-4,4)` such that `f(alpha)+f''(alpha)=0` and `f'(alpha)ne 0`

Text Solution

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The correct Answer is:
A, B, D
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