The temperature at a point $($x$,$y$,$z$)$ is given by T$($x$,$y$,$z$)=200$e$$x$2$y$2/4$z$2/9$T$($x$,$y$,$z$)=200$e$$x$2$y$2/4$z$2/9,$ where TT is measured in degrees celsius and x$,$y$,$ and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector.

Find the rate of change of the temperature at the point $(1,-1,2)$ in the direction toward the point $(-4,-2,3).$

In which direction $($unit vector$)$ does the temperature increase the fastest at $(1,-1,2)?$

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What is the maximum rate of increase of TT at $(1,-1,2)?$