Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y)

f (x,y) = sin (x,y)  & points = (1,0)

Maximum  rate of change in f at given point & direction = 1

Step-by-step 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

50

step-by-step explanation: