f(x)=x2-2x+4/9(x-1)2X属于(负无穷,1)U(1,正无穷)求f(x)最小值拜托各位大神详细过程

Question

f(x)=x2-2x+4/9(x-1)2 X属于(负无穷,1)U(1,正无穷) 求f(x)最小值拜托各位大神
详细过程

Answer 1

f(x)=x-2x+4/9(x-1) =x-2x+1+[4/9(x-1)]-1 =(x-1)+[4/9(x-1)]-1 若函数取最值,(x-1)=2/3 x-1=±√6/3 所以x=(√6/3)+1或1-√6/3