y=cosx is monotonically decreasing from 0 to 180.
Iy’I=sinx which is increasing from 0 to 90 and decreasing from 90 to 180.
dIy’I/dx needs to be positive. For above example,
dIy’I/dx=cosx which is positive from 0 to 90.
a,b positive: b<a -> b3<a3 & b4<a4
a,b negative: b<a -> b3<a3 & b4>a4