3. Short Answer Problems involving a function f : U C In => Im and a point p E U. Vf (p)? (a) (2 points) If m = 1 what is the relationship between Df(p) : Rn - R and the gradient I value at the end (of what ?! (b) (2 points) If n = 1 and m > 1 how does one think of Df (p)? more then I value at the ead. 2x y 2 (c) (2 points) If n = 3 and m = 1 can the matrix y cy x yz be the Hessian of f at ryz 22 some point (x, y, z) E U? Justify your answer. yes , because when n = 3 there is I value at the end 2 -3 4 (d) (2 points) Can you choose a value for x which makes the matrix A = 4 -8 negative (definite)? - 317 41- 4/ 7 x/ you are mesy -1 4 a team Idon't want to wore A neget - 3( - 32 - * 2 ) - 4 (4*+ 8 ) + want to make dot ( Al wystr. You can't choose a value that makes matric A ne (e) (2 points) Suppose f(x, y) = (y - 8x2) . (y - x2). Find all the critical points of f. 4 - Ex ? =0