判断函数f(x)=(x-1)^2(x-2)^3的单调区间并求其极值

Answer 1

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