Question

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that

Answer 1

Step 1:

The function is .

Definition of conservative :

In a vector field , if then F is conservative.

If F is conservative then the potential function for is .

The function is .

So F is conservative.

Step 2:

Since F is conservative, find the potential function for .

         equation (1)

          equation (2)

          equation (3)

From equation (1), equation (2) and equation (3), .

Solution :

F is conservative.

The potential function is .