Hi! If someone could help me w/ this question, I would be grateful! (I believe it involves partial derivatives, etc).

Consider the function f(x,y)=(e^x-5x)cos(y). Suppose S is the surface z=f(x,y).

(a) Find a vector which is perpendicular to the level curve of f through the point (4,4) in the direction in which f decreases most rapidly.

(b) Suppose v =4i +8j +ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4,4). What is a?

Question

Hi! If someone could help me w/ this question, I would be grateful! (I believe it involves partial derivatives, etc).

Consider the function f(x,y)=(e^x-5x)cos(y). Suppose S is the surface z=f(x,y).

(a) Find a vector which is perpendicular to the level curve of f through the point (4,4) in the direction in which f decreases most rapidly.
 
(b) Suppose v =4i +8j +ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4,4). What is a?