Question

Find the intervals of increase and decrease of the following function:
$f\left(x\right)=3x^4+8x^3+6x^2+1$

Answer 1

$f\left(x\right)=3x^4+8x^3+6x^2+1$

$\frac{d}{dx}f\left(x\right)=12x^3+24x^3+24x^2+12x=f^{\prime }\left(x\right)$

for increasing $f^{\prime }\left(x\right)>0$

$\Rightarrow 12x(x^2+2x+1)>0$

$\Rightarrow 12x(x+1{)}^2>0$

$\Rightarrow$ here $xϵ(0,\infty )$

For decreasing $f^{\prime }\left(x\right)<0$

$12x(x+1{)}^2<0$

So here internal of

$xϵ(-\infty ,0)$.