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For every twice differentiable functi...

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? There exist `r ,\ s in R` where `roo)f(x)=1` (d) There exists `alpha in (-4,\ 4)` such that `f(alpha)+f"(alpha)=0` and `f^(prime)(alpha)!=0`

A

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

B

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

C

`underset( x to oo)("lim") f(x)=1`

D

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

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The correct Answer is:
A, B, D
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