Please show all your work and highlight answer. thank you

Problem 7: Is there a direction ii in which the rate of change of f(x, 3:) = x2 - 3x32 + 4y2 at P(1,2) equal 14? Give reasons for your answer. (Ans: not possible) If such direction exists, how would you obtain the unit vector for this direction based on given conditions? Just give your thought on how to approach this problem. Problem 8: By about how much will g(x, y, z) = x + 3: cos 3 y sinz + y change if he point P(x, y, 3) moves from P.3(2, 1,0) a distance of d5 = 0.2 unit toward the point P1(0,1,2)? (Ans: 0, no change) Problem 9: Find all the local maxima, local minima, and saddle points of the following function. foxy) = 42o! - If\" -y'*