The interval, in which function y=x^3+6 x^2+6 is increasing, is - Vidyadip

MCQ

The interval, in which function $y=x^3+6 x^2+6$ is increasing, is

A
$(-\infty,-4) \cup(0, \infty)$
B
$(-\infty,-4)$
C
$(-4,0)$
D
$(-\infty, 0) \cup(4, \infty)$

✓

Answer

Given, $y=x^3+6 x^2+6 \Rightarrow \frac{d y}{d x}=3 x^2+12 x$
For increasing; $\frac{d y}{d x}>0 \Rightarrow 3 x^2+12 x>0 \Rightarrow 3 x(x+4)>0$

So, $y$ is strictly increasing in $(-\infty,-4) \cup(0, \infty)$.

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