$II.$ Consider the function $f(x,y,z)=x^{y^{z^2}}{x}^{y^{z^2}}=x^{(y^{(z^2)})}fat$ the point $(1,2,3)in$ the direction $of($:$1,1,1$:$).$

$b.In$ what direction $isf$ increasing the fastest $at$ the point $(1,2,3)$

$c.$ Whats the maximum rate $of$ change $offat$ the point $(1,2,3)$