Question

f(x)=x-e^x求极值、用导数求

f(x)=x-e^x求极值、用导数求

Answer 1

如下

Answer 2

f'(x)=1-e^x,
x<0时f'(x)>0,f(x)是增函数；
x>0时f'(x)<0,f(x)是减函数。
所以f(x)的极大值=f(0)=-1.

Answer 3

y'=1-e^x=0,得极值点x=0
当x<0时,y'>0,单调增
当x>0时,y'<0,单调减
f(0)=0-1=-1为极大值点

Answer 4

f(x)=xe^x
f'(x)=e^x+xe^x
=e^x(1+x)=0
∴x=-1
f(-1)=-1/e

∴极值是当x=-1时得极值-1/e

Answer 5

f(x)=x-e^x
f'(x) = 1-e^x
f'(x)=0
1-e^x =0
x=0
f''(x) = -e^x
f''(0) = -1 <0 max
max f(x) =f(0) = 0-e^0 = -1