Find the intervals which proves that function is upward/increase.

a) f(x)=1-x2
b) f(x)=x2-2x

f(x) is increasing if f'(x) > 0

I'll do (a)

f'(x) = -2x
f'(x) > 0 when x < 0
The graph is a parabola with vertex at (0,1) which opens downward.