Crossing the Room

You receive a response from your home planet with datails on how to escape the planet. You are directed to comect your computer to the alien computer as a means to gather information. You are told that there is a spacecraft that can get you home, but it is guarded by several gates and traps. Your computer has informed you that the raw ingredients for fuel are available, but the amount of fuel in the ship is unknown. The first step is to travel across a room that includes hidden traps in the floor. There are safe places where you must stop in ocder $10$ make z arross the room safely. The location of these safe spaces will be translated into mathematics. which you can solve, and then program into your computer. Your computer will then detail precisely where you can stop in the roon. Your computer translates the following.

Find the open intervals on which the function $f(x)=x+8\sqrt[\phantom{2}]{6-x}$ is increasing ar decressing. The safe points wh be calculsted from these intensts. $r$ the function is never hicreasing or decressing, arowite an inouf ar NA to your computer.

Increasing Intarval: $$

Decreasing Intervel: $$