Find the intervals in which the following functions are increasin… - Vidyadip

Question

Find the intervals in which the following functions are increasing or decreasing.
$f(x) = x^8 + 6x^2$

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Answer

We have $f(x) = x^8 + 6x^2$
$\therefore$ $f'(x) = 8x^7 + 12x$
Critical points $f'(x) = 0$
$\Rightarrow 8x^7 + 12x = 0$
$ \Rightarrow 4x(2x^6 + 3) = 0$
$ \Rightarrow x = 0$
Clearly, $f'(x) > 0$ if $x < 0f'(x) < 0$ if $x < 0$
Thus, $f(x)$ increases in $(0,\infty),$ decreases in $(-\infty,0).$

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