判断函数f(x)=(x-1)^2(x-2)^3的单调区间并求其极值
2016-01-13 · 知道合伙人教育行家
关注
展开全部
f(x)=(x-1)²(x-2)³
f′(x) = 2(x-1)(x-2)³+3(x-1)²(x-2)²
= (x-1)(x-2)²{2x-4+3x-3)
= (x-2)²(x-1)(5x-7)
单调增区间:(-∞,1),(7/5,+∞)
单调减区间:(1,7/5)
极大值f(1) = 0
极小值f(7/5) = (7/5-1)²(7/5-2)³ = (2/5)²(-3/5)³ = -108/3125
f′(x) = 2(x-1)(x-2)³+3(x-1)²(x-2)²
= (x-1)(x-2)²{2x-4+3x-3)
= (x-2)²(x-1)(5x-7)
单调增区间:(-∞,1),(7/5,+∞)
单调减区间:(1,7/5)
极大值f(1) = 0
极小值f(7/5) = (7/5-1)²(7/5-2)³ = (2/5)²(-3/5)³ = -108/3125
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询