The interval in which function given by $f(x)=sin^4x+cos^4x, x\in \left[0, \frac{\pi}{2}\right]$ is decreasing is :

$\left(0, \frac{\pi}{4}\right]$ $\left(0, \frac{\pi}{4}\right)$ $\left[0, \frac{\pi}{4}\right)$ $\left[0, \frac{\pi}{4}\right]$

$\left[0, \frac{\pi}{4}\right]$