Question

Determine whether or not the vector field is conservative.

Answer 1

Step 1:

The function is .

Rewrite the function.

Definition of conservative :

In a vector field , if then F is conservative..

The function is .

Here .

So F is conservative.

Step 2:

If F is conservative, then find the potential function for .

To find the potential function, follow the condition .

          equation (1)

          equation (2)

From equation (1) and equation (2), .

Solution :

F is conservative.

The potential function is .