Suppose a tub has the shape of an elliptical paraboloid given by z = ax2+by2 (where a, b are some positive constants). If a marble were released at the point (1, 1, a + b) on the inside surface of the tub, in what direction would it begin to roll? Your answer should be a unit vector in the requested direction.

It would roll in this direction.

Step-by-step explanation:

It would roll to the direction of maximum decrease, which is the -1 times the direction of maximum increase, which is given by the gradient of the function.  

Since  

For this case, the gradient of your function would be

And  -1  times the gradient of your function would be

Then, at

So it would go towards

The magnitud of that vector is

and to conclude it would roll in this direction.