Okay for homework im trying to solve the following story problem:
Near a buoy, the depth of a lake at point with coordinates (x,y) is z=200+0.02x^2-0.001y^3, where x,y and z are measured in meters. A fisherman in a boat starts at (80,60) and moves towards the buoy which is at (0,0). Is the water under the boat getting deeper or shallower when he departs?
Now im thinking I need to find the gradient vector. So Im also thinking I need the partial derivatives with respect to x,y, and z. Then I dot this with the unit vector. Im thinking the unit vector in this case is like <80-0,60-0> but since he moves towards (0,0) im thinking maybe they are both negative.
Is my thinking correct? Do I need the gradient vector? Is -80,-60 the vector I need to normalize? Am I missing anything?
Thanks for any help cause Im not sure if im right or not.