Maximum/Concave Downwards
$\frac{\mathrm{d}y}{\mathrm{d}x}=\text{0}$ and $\text{f }\!\!'\text{ }\!\!'\text{ }(x)&lt;0$
Minimum/ Concave Upwards
$\frac{\mathrm{d}y}{\mathrm{d}x}=\text{0}$ and $\text{f }\!\!'\text{ }\!\!'\!\!\text{ }(x)&gt;0$
Stationary Point of Inflexion
$\frac{\mathrm{d}y}{\mathrm{d}x}=\text{0}$ and $\text{f }\!\!'\text{ }\!\!'\text{ }(x)=0$

$\frac{\mathrm{d}y}{\mathrm{d}x}=\text{0}$ and $\text{f }\!\!'\text{ }\!\!'\text{ }(x)<0$

$\frac{\mathrm{d}y}{\mathrm{d}x}=\text{0}$ and $\text{f  }\!\!'\text{  }\!\!'\!\!\text{ }(x)>0$

$\frac{\mathrm{d}y}{\mathrm{d}x}=\text{0}$ and $\text{f  }\!\!'\text{  }\!\!'\text{ }(x)=0$

Second Derivative Test

Second Derivative Test