Functions of Several Variables

Hello all,

I dont think my lecturer illustrate the application of functions of several variables generously. I dont understand how to apply it, such as in the question below: ( I believe it is actually an easy question)

Its winter season. Let T(x,y)= 36 - (1/5)[x^2 + (y - 5)^2] be the temperature at location(x,y) in a 10ft x 10ft hotel room with a heater on at night. One corner of the room is at (0,0) and the opposite corner is at (10,10).

i)What is the domain of the temperature function?

ii)Where is the likely location of the heater?

iii)Suppose you like to sleep within the temperature range of 20celcious to 25celcious. Where would you put your bed?

iv)Determine the locations in the room where the temperature is lowest.

An advanced thank you for all the help. Really appreciate it. Ironically I manage to do everything else on the tutorial's questions except this first question.Thx!