First derivative test

In calculus, the first derivative test analyses the behaviour of a function using the signs of its derivative.[cite:@openstax2020calculus]

• If a function has a local extremum at a critical point $c$ (i.e. $f^{\prime }x=0$), then the sign of $f^{\prime }x$ must not be the same on both sides of $c$, otherwise $c$ is a saddle point.