The real function f(x)=2 x^3-3 x^2-36 x+7 is - Vidyadip

MCQ

The real function $f(x)=2 x^3-3 x^2-36 x+7$ is

A
Strictly increasing in $(-\infty,-2)$ and strictly decreasing in $(-2, \infty)$
B
Strictly decreasing in $(-2,3)$
C
Strictly decreasing in $(-\infty, 3)$ and strictly increasing in $(3, \infty)$
✓
Strictly decreasing in $(-\infty,-2) \cup(3, \infty)$

✓

Answer

Correct option: D.

Strictly decreasing in $(-\infty,-2) \cup(3, \infty)$

We have, $f(x)=2 x^3-3 x^2-36 x+7$
$\Rightarrow f^{\prime}(x)=6 x^2-6 x-36=6\left(x^2-x-6\right)$
$=6(x-3)(x+2)$
$f^{\prime}(x)=0 \Rightarrow(x-3)(x+2)=0, x=-2,3$

$\therefore f(x)$ is strictly increasing in $(-\infty,-2) \cup(3, \infty)$ and strictly

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