What is the minimum value of the directional derivative of

Question

For f(x,y) = x³ - y³ + xy, Answer the following

a. ∇f(1, -2)

b. Find the directional derivative of the function f at the point (1, -2) in the direction of the vector v^→ = (1/2)i^→-(1/2)j^→.

c. When standing on the graph o f z = f ( x, y ) above the point (1 ,-2), in which direction is the steepest upward grade on the graph.

d. What is the minimum value of the directional derivative of f at the point (1,-2).

e. Find a vector u so that D f ( 1 , - 2 ) = 0.