Question

The function $f\left(x\right)=2x^3+3x^2-12x+1$ decreases in the interval

• A. $(2,3)$
• B. $(1,2)$
• C. $(-2,1)$
• D. $(-3,-2)$

Answer 1

The correct option is C

$(-2,1)$

Determine when the given function is decreasing

Given function $f\left(x\right)=2x^3+3x^2-12x+1$

$\Rightarrow f\text{'}\left(x\right)=6x^2+6x-12$

The interval in which $f\left(x\right)$ is decreasing is given by:
$f\text{'}\left(x\right)<0$

$$\begin{gathered} \Rightarrow 6x^2+6x-12<0 \\ \Rightarrow x^2+x–2<0 \\ \Rightarrow (x+2)(x–1)<0 \end{gathered}$$

So $x\in (-2,1)$

Hence, the correct option is $\left(\mathrm{C}\right)$