Let $f ( x , y , z ) = x ^ { 2 } y + y ^ { 3 } z + x z ^ { 3 }$

Essay

Let $f ( x , y , z ) = x ^ { 2 } y + y ^ { 3 } z + x z ^ { 3 }$ and let $P ( 2,1 , - 1 )$ .(a) Find the directional derivative at $P$ in the direction of $( 1,2,3)$ .(b) In what direction does $f$ increase most rapidly?
(c) What is the maximum rate of change of $f$ at the point $P$ ?