The temperature at a point (x,y,z) is given by T(x,y,z) =200e^{x^25y^27z^2}

whereTis measured inC and x,y,z in meters.

(a)Find the rate of change of temperature(inC/m)at the point P(4,1,5) in the direction toward the point (5,3,6).

_ C/m

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

(c)Find the maximum rate of increase atP.