Function f(x)=2 x^3-9 x^2+12 x+29 is monotonically decreasing whe… - Vidyadip

MCQ

Function $f(x)=2 x^3-9 x^2+12 x+29$ is monotonically decreasing when:

A
$x < 2$
B
$x > 2$
C
$x > 3$
✓
$1 < x < 2$

✓

Answer

Correct option: D.

$1 < x < 2$

$f(x)=2 x^3-9 x^2+12 x+29$
$\Rightarrow f^{\prime}(x)=6 x^2-18 x+12$
$\Rightarrow f^{\prime}(x)=6\left(x^2-3 x+2\right)$
$\Rightarrow f^{\prime}(x)=6(x-1)(x-2)$
For $f(x)$ to be decreasing, we must have
$f ^{\prime}(x)<0$
$\Rightarrow 6(x-1)(x-2)<0$
$\Rightarrow(x-1)(x-2)<0$
$[$Since, $6>0,6(x-1)(x-2)<0 $
$\Rightarrow(x-1)(x-2)<0]$
$\Rightarrow 1$
So, $f(x)$ is decreasing for $1$

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