The temperature at a point(x, y, z)is given by T(x, y, z) = 100e^−x^2 − 3y^2 − 9z^2 where T is measured in °C and x, y, z in meters.

Question

(a) Find the rate of change of temperature at the pointP(4, −1, 5) in the direction towards the point
(5, −2, 6).
(b) In which direction does the temperature increase fastest at P?
(c) Find the maximum rate of increase at P.

Answer 1

Better review the gradient operator.
(b) greatest change in the direction ∇T
(a) change in the direction of v is ∇T • v/|v|
(c) |∇T|