The temperature at a point (x, y, z) is given by T(x, y, z) = 300e−x2...

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

T(x, y, z) = 300e^{−x² −
3y² −
9z²}

where T is measured in °C and x, y, z in meters.

(a) Find the rate of change of temperature at the point P(4, −1, 3) in the direction towards the point (6, −2, 6)

(b) In which direction does the temperature increase fastest at P?

(c) Find the maximum rate of increase at P.

Expert Solution

milcah answered 2 years ago

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