Question

All values of a for which f : R $\to R$ defined by f(x)= $x^3+a{x}^2+3x+100$ is a one one functions, are

• A. $(-\infty ,-2)$
• B. $(-\infty ,4)$
• C. $(4,-4)$
• D. $(-3,3)$

Answer 1

The correct option is D $(-3,3)$

$f^{\prime }\left(x\right)=3x^2+2ax+3$

$f^{\prime }\left(x\right)=0$ and f ( x ) > 0 $f^{\prime }\left(x\right)<0$

$3x^2+2ax+3=0$

$x=\frac{-2a\pm \sqrt{4a^2-36}}{6}$

$4a^2<36$

$a\in (-3,3)$