The temperature at a point

$($x$,$ y$,$ z$)$

is given by

T$($x$,$ y$,$ z$)=200$e$$x$23$y$27$z$2$

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

$(6,3,3).$

$$C$/$m

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

$(800$e$35,1200$e$35,5600$e$35)$

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