Y=(2-4x^2)/(1-4x^2)
y'=(-8x(1-4x^2)-(2-4x^2)*(-8x))/(1-4x^2)^2=(-8x+32x^2+16x-32x^3)/(1-4x^2)^2=
=8x/(1-4x^2)^2
x=0 точка экстремума.
y''=8((1-4x^2)^2+2x(1-4x^2)*8x)/(1-4x^2)^4=8(1+16x^4-8x^2+16x^2-64x^4)/(1-4x^2)^2
-48x^4+8x^2+1=0
48s^2-8s-1=0
s1=(4+8)/48=1/4
s2=(4-8)/48=-1/12
S>=0
s=1/4 x=-1/2 x=1/2
точки перегиба x=1/2 и x=-1/2