Question

I came across a theorem for a trivial thing

Answer 1

It is called the
Monotonicity theroem

All it says is
when

\[\frac{ dy }{ dx }>0\]
A function is decreasing

\[\frac{ dy }{ dx }<0\]
A function is increasing

Answer 2

Do you mean the function is increasing when \(\dfrac{dy}{dx}>0\) and decreasing when \(\dfrac{dy}{dx}<0\)