Question

If $f(x)=x^3-6x^2+9x+3$ be a decreasing function, then $x$ lies in

• A. $\left(-\infty ,-1\right)\cap \left(3,\infty \right)$
• B. $(1,3)$
• C. $(3,\infty )$
• D. None of these

Answer 1

Answer: (B)

$\because f\left(x\right)=x^3-6x^2+9x+3$
$\therefore f^{\prime }\left(x\right)=3x^2-12x+9$
$=3\left(x^2-4x+3\right)$
For decreasing, $f^{\prime }\left(x\right)<0$
$\Rightarrow \left(x-3\right)\left(x-1\right)<0$
$\therefore x\in \left(1,3\right)$