Question

Find the interval in which the following function is increasing or decreasing.
$f\left(x\right)=x^8+6x^2$

Answer 1

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

$f^{\prime }\left(x\right)=8x^7+12x$

$=4x(2x^6+3)$

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

$\Rightarrow 4x\underset{+ve}{\underset{}{(2x^6+3)}}>0\Rightarrow x>0$

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

$\Rightarrow 4x\underset{+ve}{\underset{}{(2x^6+3)}},0\Rightarrow x<0$