(22 points) Consider the following functionf:R2R,(x,y)|x2y(x-y1).||(a)(6 Points) Compute the gradient vector of f and the Hessian matrix of f.(b)(6 Points) Determine the set of critical points of f.(c)(10 Points) Determine whether each critical point of f is a local minimum, a local maximum, or a saddle point.2.(14 points) Consider the function f:R2R defined asf(x,y):={xyxy2,if(x,y)(0,0),0,if(x,y)=(0,0).(a)(6 Points) Let inR and v=(cos(),sin()). Compute the directional derivative of f in the direction of v at the point (0,0).(b)(8 Points) Is the function f differentiable at the point (0,0)? Fully iustifv vour answer.