1.y=(x-1)/(x^2+1),
1.y'=[x^2+1-2x(x-1)]/(x^2+1)
=(2x-x^2+1)/x^4=0
得驻点x=1+√2
求出:f(0)=-1,f(1+√2)=(√2-1)/2,f(4)=3/17
所以 最大值为(√2-1)/2和最小值为-1 .
2.y=sin2x-x x∈[-π/2,π/2]
y'=2cos2x-1=0
cos2x=1/2
2x=±π/3,x=±π/6
y(π/2)=-π/2,y(-π/2)=π/2,y(π/6)=√3/2-π/6,y(π/6)=π/6-√3/2
所以
最大值为π/2和最小值为-π/2.