Application Of Derivatives

$g(x)$ increases on $\left[\dfrac{1}{2}, 1\right]$ and $g(x)$ decreases on $\left[0, \dfrac{1}{2}\right]$

$g(x)$ decreases on $[0, 1]$

$g(x)$ increases on $[0, 1]$

$g(x)$ decreases on $\left[\dfrac{1}{2}, 1\right]$ and $g(x)$ increases on $\left[0, \dfrac{1}{2}\right]$