The temperature $at$ a point $(x,y,z)is$ given $by$

$T(x,y,z)=200e^{-x^2-5y^2-9z^2}$

where $Tis$ measured $inC$ and $x,y,z\frac{C}{m}P(4,-1,2)in$ the direction toward the point $(5,-5,6).$

$\frac{C}{m}$

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

$(c)$ Find the maximum rate $of$ increase $atP.$