The interval in which the function f(x)=2 x^3+9 x^2+ 12 x-1 is de… - Vidyadip

MCQ

The interval in which the function $f(x)=2 x^3+9 x^2+$ $12 x-1$ is decreasing, is

A
$(-1, \infty)$
B
$(-2,-1)$
C
$(-\infty,-2)$
D
$[-1,1]$

✓

Answer

We have, $f(x)=2 x^3+9 x^2+12 x-1$$
\Rightarrow f^{\prime}(x)=6 x^2+18 x+12
$
For decreasing, $f^{\prime}(x)<0$
$
\begin{array}{ll}
\therefore & 6 x^2+18 x+12<0 \\
\Rightarrow & x^2+3 x+2<0 \Rightarrow(x+1)(x+2)<0 \Rightarrow-2<x<-1
\end{array}
$So, $f(x)$ is decreasing, if $x \in(-2,-1)$.

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