Answer:
a) The gradient of a function is the vector of partial derivatives. Then
b) It's enough evaluate P in the gradient.
c) The directional derivative of f at P in direction of V is the dot produtc of and v.
d) The maximum rate of change of f at P is the magnitude of the gradient vector at P.
e) The maximum rate of change occurs in the direction of the gradient. Then
is the direction vector in which the maximum rate of change occurs at P.