For every twice differentiable function $f: R \rightarrow[-2,2]$ with $(f(0))^2+\left(f^{\prime}(0)\right)^2=85$, which of the following statement(s) is (are) TRUE ?
Select ALL correct options:
A
There exist $r, s \in R$, where $r
B
There exists $x_0 \in(-4,0)$ such that $\left|f^{\prime}\left(x_0\right)\right| \leq 1$
C
$\lim _{x \rightarrow \infty} f(x)=1$
D
There exist $\alpha \in(-4,4)$ such that $f(\alpha)+f^{\prime \prime}(\alpha)=0$ and $f^{\prime}(\alpha) \neq 0$
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