I know about the formula L(x, y) = f(x, y) + fxdx + fydy, but I'm having issues applying them in this problem, any help would be appreciated.
In a room, the temperature is given by T = f(x, t) in degrees Celsius, being x the distance from the heater and t the time passed after it has been turned on. Sensors adequately placed in the room register that (1) the temperature is rising at a rate of 1.2 C per minute, 3 meters from the heater, 5 minutes since it was turned on and (2) there is a decrease of 2 C in the temperature per meter, as we get further from the position x = 3, away from the heater, 5 minutes since it has been turned on. Estimate how much colder or hotter it will be at a distance of 2.5 meters from the heater, 6 minutes after it has been turned on. Hint: use linear approximation.