$f\left(x\right)=(x-2{)}^2{x}^n,n\in N$  then $f\left(x\right)$  has

maximum at   $x=2 \mathrm{\forall }n\in N$

minimum at  $x=2 \text{if }n$  is even only

maximum at $x=0$   if $n$  is even

minimum at $x=0$  if $n$  is even and minimum at  $x=2$  $\mathrm{\forall }n\in N$