Given $f ( x , y ) = \frac { 1 } { 4 } x ^ { 4 } y ^ { 3 }$

Essay

Given $f ( x , y ) = \frac { 1 } { 4 } x ^ { 4 } y ^ { 3 }$ , at the point $( - 1,2 )$ . Find
(a) the maximum value of the directional derivative and
(b) the unit vector in the direction in which the directional derivative takes on its maximum value.