that is where the first dervitive is positive
take dervitive
[tex]f'(x)=4x-4x^3[/tex]
find the zeroes and find the signs by plugging in values between
f'(x)=0, 0=4x-4x^3, 0=(4x)(1-x^2), 0=(4x)(1-x)(1+x), x=-1, 0, 1
by subsituting values for x in the ranges and seeing the signs of the factors we get
to the left of -1, f'(x) is positive
between -1 and 0, f'(x) is negative
between 0 and 1, f'(x) is positive
to the right of 1, f'(x) is negative
so it increasing to the left of -1 and in between 0 and 1
increasing on the interval (-∞,-1) U (0,1)
