y=cosx is monotonically decreasing from 0 to 180.

y’=-sinx

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 -> b^{3}<a^{3}& b^{4}<a^{4}

a,b negative: b<a -> b^{3}<a^{3}& b^{4}>a^{4}