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The temperature at a point (x, y, z) is given by T(x, y, z) = 100e−x2 − 3y2 − 7z2 where T...

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Basic Math

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 pointP(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 atP?


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

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