For every twice differentiable function `f: R to [-2,2]` with `(f^(0))^(2)` =85 , which of the following statement(s) is (are) TRUE ?
(1) There exist`r , s in R, where r lt s,` such that f is one-one on the open interval (r,s)
(2) There exist `x_(0) in (-4,0)` such that `|f(x_(0))|le1`
`lim_( x to oo) f(x)=1`
There exist ` alpha in (-4,4)` such that `f(alpha) +f'' (alpha)=0 and f'(alpha) ne 0`

Options

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`

Answer

A, B, D