The intervals for which $f(x)=x^4-2 x^2$ is increasing are :

$(-1,0) \cup(1, \infty)$

$f(x)=x^4-2 x^2$

to check increasing / decreasing natural

we need

$f'(x) =4 x^3-4 x$

$=4 x\left(x^2-1\right)$

$=4 x(x-1)(x+1)$

$f'(x) =0$  when  $x=-1,0,1$

using waly curve method

x < -1           f(x) < 0 (decreasing)

-1 < x < 0     f(x) > 0 (increasing)

0 < x < 1      f(x) < 0 (decreasing)

x > 1            f(x) > 1 (Increasing)