Question

If $f\left(x\right) = \frac{a^{2} -1}{a^{2} +1} x^{3} -3x +5 $ is a decreasing function of $x$ in $R$, then the set of possible values of a (independent of $x$) is

• A. $(1, \infty)$
• B. $(- \infty , - 1 )$
• C. $[-1,1]$
• D. None of these

Answer 1

Answer: (C)

$f'(x)=3\left(\frac{a^{2}-1}{a^{2}+1}\right) x^{2}-3$
$f'(x) < 0$ for all $x $ if $a^{2}-1 \leq 0$
$ \Rightarrow -1 \leq a \leq 1$