f(x)=x^3-1/2x^2-2x+5
f'(x)=3x^2-x-2
令f'(x)=0
3x^2-x-2=0
（3x+2）(x-1)=0
x=-2/3,x=1
f'(x)>0 => -2/3f'(x)<0 => x<-2/3,或x>1
所以f(x)在（负无穷,-2/3）并（1,正无穷）上单调增
在（-2/3,1）上单调减
f(-2/3)=-8/27-1/2*4/9-2*(-2/3)+5
=5又22/27
f(1)=1-1/2-2+5=7/2
所以f(x)的极大值为5又22/27
极小值为7/2