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)

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