Check if a utility function represents a monotone preference

Using this definition of monotone preferences (Thanks to User Art). Let $Xsubseteq mathbb{R}^n$ be the set of possible consumption bundles, and $x,yin X$. We have weak monotone preferences if $y>>x implies ysucc x $, and strict preferences if $ygeq x implies ysucc x$. If we have a utility function $u: Xto mathbb{R}$, then $ysucc x$ is the same as $u(y)> u(x)$.

Regarding notation for two bundles $x,yin X, x=(x_1,x_2,...,x_n), y=(y_1,y_2,...,y_n)$, we say $y>>x$ if $y_i>x_i$ forall $i=1,2,...,n$ and we say $ygeq x$ if $y_igeq x_i$ forall $i=1,2,...,n$ and there is a $j$, such that $y_j>x_j$. (This notation is not universal)

Now, see if you can use this to answer your question