Determine whether the vector field is Conservative. if it is, find a potential function for the vector field.

Question

Determine whether the vector field is <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Conservative. if it is, find a potential function for the vector field.

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 functio, follow the condition .

         equation (1)

          equation (2)

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

Solution :

F is conservative.

The potential function is .