Question

判断下列函数的单调性，并求出单调区间

(1)f(x)=x^2+2x-4
(2)f(x)=2x^2-3x+3

(3)f(x)=3x+x^3

(4)f(x)=x^3+x^2-x

Answer 1

1. f'(x)=2x+2
当 X>=-2, f'(x)>=0, f(x) 单调递增；当 X<=-2, f'(x)<=0, f(x) 单调递减
2.f'(x)=4x-3
当 X>=3/4, f'(x)>=0, f(x) 单调递增；当 X<=3/4, f'(x)<=0, f(x) 单调递减
3.f'(x)=3+2x^2>0
f(x) 单调递增
4.f'(x)=3x^2+2x-1=(3x-1)(x+1)
当 X>=1/3或x<=-1, f'(x)>=0, f(x) 单调递增；当 -1<=X<=1/3, f'(x)<=0, f(x) 单调递减