Exercises: Derivatives 4 – "Math for Non-Geeks"

Criterion for constancy

Hint

Since $f''=(f')'=(\omega g)'=\omega g'=-\omega ^{2}f$ and analogously $g''=-\omega ^{2}g$ both the functions $f$ and $g$ satisfy the differential equation $f''+\omega f=0$ (or $g''+\omega g=0$).

Monotonicity criterion

Hint

Similarly, we can show that $f$ is strictly monotonically decreasing in the cases $a=b=0$ and $c<0$, as well as for $a<0$ and $3ac>b^{2}$.