Find the maximum rate of change of $f ( x , y ) = x y ^ { 2 } + \sqrt { y }$ at the point $( 2,1 )$. In what direction does it occur?

Name: Find the maximum rate of change of $f ( x , y ) = x y ^ { 2 } + \sqrt { y }$ at the point $( 2,1 )$. In what direction does it occur?
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The Answer of Find the maximum rate of change of $f ( x , y ) = x y ^ { 2 } + \sqrt { y }$ at the point $( 2,1 )$. In what direction does it occur?

Find the Maximum Rate of Change Of f(x,y)=xy2+yf ( x , y ) = x y ^ { 2 } + \sqrt { y }f(x,y)=xy2+y​

Find the Maximum Rate of Change Of $f ( x , y ) = x y ^ { 2 } + \sqrt { y }$