Answer:
Maximum rate of change at the point (-1,2) = √17
Direction is the direction of the gradient
Step-by-step explanation:
The gradient of a function (scalar or vectorial ) is a vector in the direction of maximum rate of change then
f( x,y ) =  x*2y  + 2y
grad    =  δ/δx i +  δ/δy j + δ/δz k
grad f(x,y)  = [ δ/δx i , δ/δy]  =  [ 2y , x+2 ]
at the point  ( -1 , 2 )
grad f(x,y)  = [4 , 1]
| grad f(x,y) |  =  √ (4)²  + (1)²   =  √17
 
        
             
        
        
        
I hope this picture helps.