y'=4x^3-4x
y'=4x(x^2-1)
y'=4x(x-1)(x+1)
y'=0
4x(x-1)(x+1)=0
4x=0rArrx=0
x-1=0rArrx=1
x+1=0rArrx=-1
color(brown)(y'<0)
color(brown)(-oo< x< -1 and 0 < x <1)
color(blue)(y'>0)
color(blue)(-1< x < 0 and 1 < x <+oo)
So,
the function
y decreases for color(brown)(-oo < x <-1) reaching the point (-1,2)
y increases for color(blue)(-1< x <0)
So,(color(red)(-1,2)) is a local minimum
y increases for color(blue)(-1< x <0) reaching the point(0,3)
then it decreases color(brown)(0 < x <1)
So,(color(red)(0,3)) is a local maximum
y decreases for color(brown)(0 < x <1) reaching the point(1,2)then
y increases for color(blue)(1< x < oo)
So,(color(red)(-1,2)) is a local minimum
