Let $fbe$ the $R^3-R$ function defined $by$

$f(x,y,z)=x^{yz}$

$(a)$ Determine the rate $of$ increase $offat$ the point $(e,1,1)in$ the direction $of$ the

vector $(3,-2,1).$

$(b)$ Determine the maximum rate $of$ increase $offat(e,1,1).In$ which direction $is$ the maxi$-$

mum rate $of$ increase?

$(c)At$ the point $(e,1,1),in$ which direction $is$ the function constant $(i.e.$ its value doesn't

change$)?$