QUESTION 1 Let /(I, y) = V/2x -y. (a). Find the directional derivative of f at the point (-3,3) in the direction of the vector . (b). In which direction does f increase most quickly at the point (-3,3)? What is this maximal rate of increase? QUESTION 2 Is there a point on the sphere s' + y' + 2' -9 at which the tangent plane is parallel to the plane 2x + 2y - = = 10? If so, find it. QUESTION 3 Suppose that the temperature at a point (I, y, 2) is given by T(I, y, =) = 80 + (a). Find the rate of change of the temperature at the point (1, -2, 1) in the diree- tion of the vector . (b). At the point (1, -2, 1), in which direction does the temperature increase most quickly? What is that maximum rate of change of temperature? QUESTION 4 Find equations for the tangent plane and normal line to the surface s' + y' 2sin(z) at the point (1, -1, #/2). QUESTION 5 Consider the cone 2 - s' -y' and the sphere s' ty +2' -18. They intersect at the point (-3, 3,0), among others. Find the angle (or the cosine of the angle) between these surfaces at the point (-3,3, 0). Hint: the angle between two surfaces is the same as the angle between their normal lines