Function f(x)=2 x^3-15 x^2+36 x+6 is increasing in which of inter…

MCQ

Function $f(x)=2 x^3-15 x^2+36 x+6$ is increasing in which of interval :

✓
$(-\infty, 2) \cup(3, \infty)$
B
$(-\infty, 2)$
C
$(-\infty, 2] \cup[3, \infty)$
D
$[3, \infty)$

✓

Answer

Correct option: A.

$(-\infty, 2) \cup(3, \infty)$

(A)
$
\begin{aligned}
f(x) & =2 x^3-15 x^2+36 x+6 \\
f^{\prime}(x) & =6 x^2-30 x+36 \\
& =6\left(x^2-5 x+6\right)
\end{aligned}
$
$
=6(x-2)(x-3)
$
$f(x)$ is increasing if $f^{\prime}(x)>0$
$
\begin{array}{lc}
\Rightarrow & 6(x-2)(x-3)>0 \\
\Rightarrow & x \in(-\infty 2) \cup(3, \infty)
\end{array}
$

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