Question

求单调区间

1，f（x）=x+1/x
2，f（x）=x-1/x
3，f（x）=x+16/x
4，f（x）=1/x2-2*x+3

Answer 1

1.f(x)=x+1/x
f'(x)=1-1/x^2
f'(x)＞0
1-1/x^2＞0
x^2＞1
x＜-1或x＞1
f(x)=x+1/x在(-∞,-1)∪(1,+∞)上为单调递增，在(-1,1)上为单调递减
2.f(x)=1-1/x
f'(x)=1+1/x^2
f'(x)＞0
1+1/x^2恒大于0
f(x)=x-1/x在R上未单调递增
3.f(x)=x+16/x
f'(x)=1-16/x^2
f'(x)＞0
1-16/x^2＞0
x^2＞16
x＜-4或x＞4
f(x)=x+16/x在(-∞,-4)∪(4,﹢∞)上为单调递增，在(-4,4)上为单调递减
4.f(x)=1/x^2-2*x+3
f'(x)=-2/x^3-2
f'(x)＞0
-2/x^3-2＞0
x＜-1
f(x)=1/x^2-2*x+3在(-∞,-1)上为单调递增，在(-1,+∞)上为单调递减

Answer 2