Let $f ( x , y ) = \sqrt { 2 x + 3 y }$

Essay

Let $f ( x , y ) = \sqrt { 2 x + 3 y }$ .(a) In which direction does $f$ increase most rapidly at the point $( 3,1 )$ ?
(b) What is the maximum rate of change of $f$ at the point $( 3,1 )$ ?
(c) Find a unit vector $\mathbf { u }$ such that $D _ { u } f = 0$ at $( 3,1 )$ .