Paragraph: Consider the function $f(x)=3 x^4-20 x^3-12 x^2+288 x+1$
Question: In which one of the following intervals is the function decreasing?

• A

  $(-2,3)$
• Correct answer
  B

  $(3,4)$
• C

  $(4,6)$
• D

  $(6,9)$

Solution

$\begin{aligned} & f^{\prime}(x) \lt 0 \\ & (x+2)(x-3)(x-4) \lt 0\end{aligned}$
$\Rightarrow x \in(-\infty,-2) \cup(3,4)$

Hence, the correct answer is option: 'B'.