He 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(4, −1, 4) in the direction towards the point (6, −4, 5). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.

Answer with Step-by-step explanation:

We are given that

a.We have to find the rate of change of temperature at the point P(4,-1,4) in the direction towards the point (6,-4,5).

Substitute x=4,y=-1 and z=4

Rate of change of temperature at point P(4,-1,4) in the direction of the point (6,-4,5)=

Rate of change of temperature at point P(4,-1,4) in the direction of the point (6,-4,5)=

b.The temperature increases fastest in the direction of

c.Maximum rate of increase at P=

Maximum rate of increase at P=

fwms@lil_ben06

step-by-step explanation: