求y最值,y=x(1-x2),x2指的是X的平方,要用基本不等式

y2=x2(1-x2)2,若求出y2的最值,y的最值亦可得出,
y2=x2(1-x2)2=1/2(2x2*(1-x2)*(1-x2))<=1/2[1/3(2x2+(1-x2)+(1-x2))]3=(2/3)3=4/27,所以y2的最大值为4/27,y的最值即为4/27的平方根

y^2=x^2*(1-x^2)*(1-x^2)
=2x^2*(1-x^2)*(1-x^2)*0.5
≤[(2x^2+1-x^2+1-x^2)/3]^3*0.5
=4/27
y<=2/3根号3
取等号时 2x^2=1-x^2 x=1/根号3

没有说y>0,千年幽影是不对的

y^2=x^2*(1-x^2)*(1-x^2)
=2x^2*(1-x^2)*(1-x^2)*0.5
≤[(2x^2+1-x^2+1-x^2)/3]^3*0.5
=4/27
-2根号3/9 <=y<=2根号3/9