The temperature at a point (x, y, z) is given by T(x, y, z)

Last updated: 7/16/2022

The temperature at a point (x, y, z) is given by T(x, y, z) = 400e^(-x²-5y²-9z²) where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature (in °C/m) at the point P(2, -1, 4) in the direction toward the point (3, -5, 6). (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.