Gradient of Scalar - Find Direction for Mosquito (1,1,2)

[bigmoe70]

The temperature in an auditorium is given by T = x² + y² - z. A mosquito located at (1,1,2) in the auditorium desires to fly in such a direction that it will get warm as soon as possible. In what direction must it fly?

I know that the gradient of T will point to the direction where the temperature rises the fastest, but I'm not quite sure what to do with the point they give me (1,1,2).

 

[Defennder]

I believe the direction they are asking for is the initial direction from its starting location of (1,1,2). The gradient of the temperature function isn't a constant, so the direction at anyone point in the auditorium may vary so giving you that initial position is a way of saying "Give me definite direction to fly towards."