Answer:
f (x,y) = sin (x,y) & points = (1,0)
Maximum rate of change in f at given point & direction = 1
Explanation:
The function & points are not given,
Considering them as general example : f (x,y) = sin (x,y) & points = (1,0)
Maximum rate of change in f (x,y) happens in direction of ∇ f (1,0)
∇ f (x,y) = [ df / dx , df/ dy ]
= [ y cos (xy) , x cos (xy) ]
∇ f (1,0) = [ 0, cos (0) ] = (0,1)
Magnitude at (1,0) = ∇ f (1,0) = √ 0^2 + 1^2 = 1