10.

Consider the function f(x, y) = (ex - 3x) cos(y). Suppose S is the surface = = f(c, y). (a) Find a vector which is perpendicular to the level curve of f through the point (4, 2) in the direction in which f decreases most rapidly. vector = (b) Suppose v = 1i + 17 + ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4, 2). What is a? Note: You can earn partial credit on this