Q4. Let f(r, y) be differentiable at (0,0). Suppose i. f increases most rapidly in the direction of the vector (1, 3) at the point (0, 0). ii. Duf (0,0) = -1, where u = (7-yz Find unit vector(s) v satisfying the following properties, or explain why no such v exists. a. Dy f (0, 0) is minimum. b. Dy f (0,0) = 0. c. Dy / (0, 0) = -3. Q5. Let f : R- - R be a function. Fix a point (To, yo). Consider a linear approximation of /(r, y) near (To, 30), defined by I(r, y) = /(ro. yo) +r(r - To) + s(y - yo). where r, s e R are constants. Suppose the error (I, y) = f(x. y) - f(To. yo) - r(I - To) - s(y - yo) satisfies lim E(r, y) = 0. (I,y) +(20,Do) (x - To)- + (y - 90)- Show that the partial derivatives fr(To. yo) and fy(To, yo) exist with r = fx(To.yo) and s = fy(To. yo)