Task 3 Let f (x, y) = xy2 be a function with the definition set de (x, y) so that 2 x2 + y2 = 6 a) Explain how we can know that f has the definition set of maximum point and minimum point. Explain why f does not have stationary points. b) Determine the largest and smallest value of f using the Lagrange method. c) What is the answer to parts a) and b) if the definition set is 2x2 + y2 s 6? d) Let h: RR be a function given by h (x, y) = 4-x2 - y2. i) Find the level curve of f at point P (1, -1). Determine Vh (1, -1). Draw the point P, as well as the level curve and the gradient to h at this point. ii) Calculate how fast h changes at point P in the direction V = -37 +47 iii) In which direction from point P is this change greatest? (Hint: the direction can be given as a vector)