(1)设函数f(x)=xlnx+(1-x)ln(1-x)(0<x<1),求f(x
题型:解答题
问题:
(1)设函数f(x)=xlnx+(1-x)ln(1-x)(0<x<1),求f(x)的最小值;
(2)设正数p1,p2,p3,…,p2n满足p1+p2+p3+…+p2n=1,求证:p1lnp1+p2lnp2+p3lnp3+…+p2nlnp2n≥-n.
(1)设函数f(x)=xlnx+(1-x)ln(1-x)(0<x<1),求f(x)的最小值;
(2)设正数p1,p2,p3,…,p2n满足p1+p2+p3+…+p2n=1,求证:p1lnp1+p2lnp2+p3lnp3+…+p2nlnp2n≥-n.