I can't quite figure out where to begin / find an equation for this problem.... I need a good push in the right direction, thanks ahead of time.The temperature at a point (x, y, z) is given by the following equation where T is measured in °C and x, y, z in meters. T(x, y, z) = 200e^((-x^2)(-3y^2)(-9z^2))
(a) Find the rate of change of temperature at the point P(2, -1, 2) in the direction towards the point (3, -3, 3).
(b) In which direction does the temperature increase fastest at P?
(c) Find the maximum rate of increase at P.
What equation do I need to use, in terms of the given variables in my problem??