A. Choose a specific point P₀ = (a, b, f(a,b)) on the surface z = f(x,y), other than (0,0,0).

1. Calculate the gradient of fat (a,b). Show your work.

2. Calculate the unit vector in which f increases most rapidly at (a,b). Show your work.

3. Calculate the directional derivative of f at (a,b) in the direction of greatest increase. Show your work.

4. Determine the two unit vectors in which the directional derivative of f at (a,b) is equal to zero. Show your work.

The point will be a = 2 and b = 4