g(x)=-x2+(4-k)x+12,g'(x)=-2x+4-k,在区间[-2,2]上g'(x)∈[-k,8-k]；
要使函数g(x)在区间上是单调函数,只要g'(x)恒正或恒负,即k∈(-∞,0]∪[8,+∞)