Question

найти экстремум функции y=(x-1)^2/x^2+1

Answer 1

$y' = frac{2(x-1)(x^2+1)-2x(x-1)^2}{(x^2+1)^2} =0\ 2x^3-2x^2+2x-2-2x^3+4x^2-2x=0\ 2x^2-2=0\ x^2=1\ x_1=-1\ x_2=1\ f(-1)= frac{4}{2} =2 - max\ f(1)=0 - min$