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.

step-by-step explanation:

compare

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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