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 $P$ ?

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The Answer of 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 $P$ ?

Let f(x,y,z)=x2y+y3z+xz3f ( x , y , z ) = x ^ { 2 } y + y ^ { 3 } z + x z ^ { 3 }f(x,y,z)=x2y+y3z+xz3

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