Snap summary of tests using $y'$ and $y''$ (for inflexions)

$y'$ TEST: STATIONARY POINTS - NATURE

 ROW 1 - HORIZONTAL INFLEXION

 ROW 2 - HORIZONTAL INFLEXION

 ROW 3 - MINIMUM TURNING POINT

 ROW 4 - MAXIMUM TURNING POINT

$y''$ TEST FOR AN INFLEXION:

 ROW 5 - CONFIRMED INFLEXION

 ROW 6 - CONFIRMED INFLEXION

 ROW 7 - NOT AN INFLEXION

 ROW 8 - NOT AN INFLEXION