(Solved): You receive a response from your home planet with details on how to escape the planet. You are dire ...

You receive a response from your home planet with details on how to escape the planet. You are directed to connect 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 order to make it across 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 room. Your computer translates the following: Find the open intervals on which the function \\( f(x)=x+10 \\sqrt{4-x} \\) is increasing or decreasing. The safe points will be calculated from these intervals. If the function is never increasing or decreasing, provide an input of NA to your computer. Increasing Interval: ? Decreasing Interval: ? Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.