#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
