The temperature at a point (x, y, z) is given by T(x, y, z) = 100e−x2...

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

T(x, y, z) = 100e^{−x² −
3y² −
7z²}

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

(a) Find the rate of change of temperature at the point P(2, −1, 2) in the direction towards the point (4, −4, 4). answer in °C/m

(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

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

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