因?yàn)閒(x)=x^2+2ax+2,且x∈[-5,5].
則有：f'(x)=2x+2a
(1)若要使f(x)單調(diào)增,有：f'(x)＞0
即：2x+2a＞0
則有：a＞-x
因?yàn)閤∈[-5,5],所以a＞-5
即：當(dāng)a∈(-5,∞)時(shí),f(x)單調(diào)增.
(2)若要使f(x)單調(diào)減,有：f'(x)＜0
即：2x+2a＜0,
則有：a＜-x
因?yàn)閤∈[-5,5],所以a＜-5
即：當(dāng)a∈(-∞,-5)時(shí),f(x)單調(diào)減.