f(x)=(x^2-1)e^x的单调区间与极值
1个回答

f'(x)=(x^2+2x-1)e^x

=(x+1+√2)(x+1-√2)e^x,

x.-1-√2.-1+√2...

f'(x).+.-.+

f(x).↑.↓.↑

∴f(x)的增区间是(-∞,-1-√2),(-1+√2,+∞);减区间是(-1-√2,-1+√2),

f(x)的极大值=f(-1-√2)

=(2+2√2)e^(-1-√2),

f(x)的极小值=f(-1+√2)

=(2-2√2)e^(-1+√2).